Algebra Examples

$(4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Step 1

Simplify $(4 - 5 x) (4 x - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + (4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Step 1.2

Simplify by adding zeros.

$(4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Step 1.3

Expand $(4 - 5 x) (4 x - 5)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$4 (4 x - 5) - 5 x (4 x - 5) = (10 x - 3) (7 - 2 x)$

Step 1.3.2

Apply the distributive property.

$4 (4 x) + 4 \cdot - 5 - 5 x (4 x - 5) = (10 x - 3) (7 - 2 x)$

Step 1.3.3

Apply the distributive property.

$4 (4 x) + 4 \cdot - 5 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $4$ by $4$ .

$16 x + 4 \cdot - 5 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.2

Multiply $4$ by $- 5$ .

$16 x - 20 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.3

Rewrite using the commutative property of multiplication.

$16 x - 20 - 5 \cdot 4 x \cdot x - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1.4.1

Move $x$ .

$16 x - 20 - 5 \cdot 4 (x \cdot x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.4.2

Multiply $x$ by $x$ .

$16 x - 20 - 5 \cdot 4 x^{2} - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.5

Multiply $- 5$ by $4$ .

$16 x - 20 - 20 x^{2} - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Step 1.4.1.6

Multiply $- 5$ by $- 5$ .

$16 x - 20 - 20 x^{2} + 25 x = (10 x - 3) (7 - 2 x)$

Step 1.4.2

Add $16 x$ and $25 x$ .

$41 x - 20 - 20 x^{2} = (10 x - 3) (7 - 2 x)$

Step 2

Simplify $(10 x - 3) (7 - 2 x)$ .

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Step 2.1

Expand $(10 x - 3) (7 - 2 x)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x (7 - 2 x) - 3 (7 - 2 x)$

Step 2.1.2

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x \cdot 7 + 10 x (- 2 x) - 3 (7 - 2 x)$

Step 2.1.3

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x \cdot 7 + 10 x (- 2 x) - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $7$ by $10$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 x (- 2 x) - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2.1.2

Rewrite using the commutative property of multiplication.

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 x \cdot x - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1.3.1

Move $x$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 (x \cdot x) - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2.1.3.2

Multiply $x$ by $x$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 x^{2} - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2.1.4

Multiply $10$ by $- 2$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 3 \cdot 7 - 3 (- 2 x)$

Step 2.2.1.5

Multiply $- 3$ by $7$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 21 - 3 (- 2 x)$

Step 2.2.1.6

Multiply $- 2$ by $- 3$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 21 + 6 x$

Step 2.2.2

Add $70 x$ and $6 x$ .

$41 x - 20 - 20 x^{2} = 76 x - 20 x^{2} - 21$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $76 x$ from both sides of the equation.

$41 x - 20 - 20 x^{2} - 76 x = - 20 x^{2} - 21$

Step 3.2

Add $20 x^{2}$ to both sides of the equation.

$41 x - 20 - 20 x^{2} - 76 x + 20 x^{2} = - 21$

Step 3.3

Combine the opposite terms in $41 x - 20 - 20 x^{2} - 76 x + 20 x^{2}$ .

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Step 3.3.1

Add $- 20 x^{2}$ and $20 x^{2}$ .

$41 x - 20 - 76 x + 0 = - 21$

Step 3.3.2

Add $41 x - 20 - 76 x$ and $0$ .

$41 x - 20 - 76 x = - 21$

Step 3.4

Subtract $76 x$ from $41 x$ .

$- 35 x - 20 = - 21$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $20$ to both sides of the equation.

$- 35 x = - 21 + 20$

Step 4.2

Add $- 21$ and $20$ .

$- 35 x = - 1$

Step 5

Divide each term in $- 35 x = - 1$ by $- 35$ and simplify.

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Step 5.1

Divide each term in $- 35 x = - 1$ by $- 35$ .

$\frac{- 35 x}{- 35} = \frac{- 1}{- 35}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 35$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 35 x}{- 35} = \frac{- 1}{- 35}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 35}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{35}$

Decimal Form:

$x = 0.0\overline{285714}$