Algebra Examples

$(3 x - 4) (4 x - 3) = (6 x - 4) (2 x - 5)$

Step 1

Simplify $(3 x - 4) (4 x - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + (3 x - 4) (4 x - 3) = (6 x - 4) (2 x - 5)$

Step 1.2

Simplify by adding zeros.

$(3 x - 4) (4 x - 3) = (6 x - 4) (2 x - 5)$

Step 1.3

Expand $(3 x - 4) (4 x - 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$3 x (4 x - 3) - 4 (4 x - 3) = (6 x - 4) (2 x - 5)$

Step 1.3.2

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 3 - 4 (4 x - 3) = (6 x - 4) (2 x - 5)$

Step 1.3.3

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 3 - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

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

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x + 3 x \cdot - 3 - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

Move $x$ .

$3 \cdot 4 (x \cdot x) + 3 x \cdot - 3 - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.2.2

Multiply $x$ by $x$ .

$3 \cdot 4 x^{2} + 3 x \cdot - 3 - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.3

Multiply $3$ by $4$ .

$12 x^{2} + 3 x \cdot - 3 - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.4

Multiply $- 3$ by $3$ .

$12 x^{2} - 9 x - 4 (4 x) - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.5

Multiply $4$ by $- 4$ .

$12 x^{2} - 9 x - 16 x - 4 \cdot - 3 = (6 x - 4) (2 x - 5)$

Step 1.4.1.6

Multiply $- 4$ by $- 3$ .

$12 x^{2} - 9 x - 16 x + 12 = (6 x - 4) (2 x - 5)$

Step 1.4.2

Subtract $16 x$ from $- 9 x$ .

$12 x^{2} - 25 x + 12 = (6 x - 4) (2 x - 5)$

Step 2

Simplify $(6 x - 4) (2 x - 5)$ .

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Step 2.1

Expand $(6 x - 4) (2 x - 5)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$12 x^{2} - 25 x + 12 = 6 x (2 x - 5) - 4 (2 x - 5)$

Step 2.1.2

Apply the distributive property.

$12 x^{2} - 25 x + 12 = 6 x (2 x) + 6 x \cdot - 5 - 4 (2 x - 5)$

Step 2.1.3

Apply the distributive property.

$12 x^{2} - 25 x + 12 = 6 x (2 x) + 6 x \cdot - 5 - 4 (2 x) - 4 \cdot - 5$

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

Rewrite using the commutative property of multiplication.

$12 x^{2} - 25 x + 12 = 6 \cdot 2 x \cdot x + 6 x \cdot - 5 - 4 (2 x) - 4 \cdot - 5$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$12 x^{2} - 25 x + 12 = 6 \cdot 2 (x \cdot x) + 6 x \cdot - 5 - 4 (2 x) - 4 \cdot - 5$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$12 x^{2} - 25 x + 12 = 6 \cdot 2 x^{2} + 6 x \cdot - 5 - 4 (2 x) - 4 \cdot - 5$

Step 2.2.1.3

Multiply $6$ by $2$ .

$12 x^{2} - 25 x + 12 = 12 x^{2} + 6 x \cdot - 5 - 4 (2 x) - 4 \cdot - 5$

Step 2.2.1.4

Multiply $- 5$ by $6$ .

$12 x^{2} - 25 x + 12 = 12 x^{2} - 30 x - 4 (2 x) - 4 \cdot - 5$

Step 2.2.1.5

Multiply $2$ by $- 4$ .

$12 x^{2} - 25 x + 12 = 12 x^{2} - 30 x - 8 x - 4 \cdot - 5$

Step 2.2.1.6

Multiply $- 4$ by $- 5$ .

$12 x^{2} - 25 x + 12 = 12 x^{2} - 30 x - 8 x + 20$

Step 2.2.2

Subtract $8 x$ from $- 30 x$ .

$12 x^{2} - 25 x + 12 = 12 x^{2} - 38 x + 20$

Step 3

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

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Step 3.1

Subtract $12 x^{2}$ from both sides of the equation.

$12 x^{2} - 25 x + 12 - 12 x^{2} = - 38 x + 20$

Step 3.2

Add $38 x$ to both sides of the equation.

$12 x^{2} - 25 x + 12 - 12 x^{2} + 38 x = 20$

Step 3.3

Combine the opposite terms in $12 x^{2} - 25 x + 12 - 12 x^{2} + 38 x$ .

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Step 3.3.1

Subtract $12 x^{2}$ from $12 x^{2}$ .

$- 25 x + 12 + 0 + 38 x = 20$

Step 3.3.2

Add $- 25 x + 12$ and $0$ .

$- 25 x + 12 + 38 x = 20$

Step 3.4

Add $- 25 x$ and $38 x$ .

$13 x + 12 = 20$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$13 x = 20 - 12$

Step 4.2

Subtract $12$ from $20$ .

$13 x = 8$

Step 5

Divide each term in $13 x = 8$ by $13$ and simplify.

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Step 5.1

Divide each term in $13 x = 8$ by $13$ .

$\frac{13 x}{13} = \frac{8}{13}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $13$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{8}{13}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{13}$

Decimal Form:

$x = 0.\overline{615384}$