Algebra Examples

$(3 x - 2) (x + 4) - 3 (x + 5) (x - 1) = 0$

Step 1

Simplify $(3 x - 2) (x + 4) - 3 (x + 5) (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(3 x - 2) (x + 4)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$3 x (x + 4) - 2 (x + 4) - 3 (x + 5) (x - 1) = 0$

Step 1.1.1.2

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 4 - 2 (x + 4) - 3 (x + 5) (x - 1) = 0$

Step 1.1.1.3

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 4 - 2 x - 2 \cdot 4 - 3 (x + 5) (x - 1) = 0$

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

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

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Step 1.1.2.1.1.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 4 - 2 x - 2 \cdot 4 - 3 (x + 5) (x - 1) = 0$

Step 1.1.2.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot 4 - 2 x - 2 \cdot 4 - 3 (x + 5) (x - 1) = 0$

Step 1.1.2.1.2

Multiply $4$ by $3$ .

$3 x^{2} + 12 x - 2 x - 2 \cdot 4 - 3 (x + 5) (x - 1) = 0$

Step 1.1.2.1.3

Multiply $- 2$ by $4$ .

$3 x^{2} + 12 x - 2 x - 8 - 3 (x + 5) (x - 1) = 0$

Step 1.1.2.2

Subtract $2 x$ from $12 x$ .

$3 x^{2} + 10 x - 8 - 3 (x + 5) (x - 1) = 0$

Step 1.1.3

Apply the distributive property.

$3 x^{2} + 10 x - 8 + (- 3 x - 3 \cdot 5) (x - 1) = 0$

Step 1.1.4

Multiply $- 3$ by $5$ .

$3 x^{2} + 10 x - 8 + (- 3 x - 15) (x - 1) = 0$

Step 1.1.5

Expand $(- 3 x - 15) (x - 1)$ using the FOIL Method.

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Step 1.1.5.1

Apply the distributive property.

$3 x^{2} + 10 x - 8 - 3 x (x - 1) - 15 (x - 1) = 0$

Step 1.1.5.2

Apply the distributive property.

$3 x^{2} + 10 x - 8 - 3 x \cdot x - 3 x \cdot - 1 - 15 (x - 1) = 0$

Step 1.1.5.3

Apply the distributive property.

$3 x^{2} + 10 x - 8 - 3 x \cdot x - 3 x \cdot - 1 - 15 x - 15 \cdot - 1 = 0$

Step 1.1.6

Simplify and combine like terms.

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Step 1.1.6.1

Simplify each term.

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Step 1.1.6.1.1

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

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Step 1.1.6.1.1.1

Move $x$ .

$3 x^{2} + 10 x - 8 - 3 (x \cdot x) - 3 x \cdot - 1 - 15 x - 15 \cdot - 1 = 0$

Step 1.1.6.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} + 10 x - 8 - 3 x^{2} - 3 x \cdot - 1 - 15 x - 15 \cdot - 1 = 0$

Step 1.1.6.1.2

Multiply $- 1$ by $- 3$ .

$3 x^{2} + 10 x - 8 - 3 x^{2} + 3 x - 15 x - 15 \cdot - 1 = 0$

Step 1.1.6.1.3

Multiply $- 15$ by $- 1$ .

$3 x^{2} + 10 x - 8 - 3 x^{2} + 3 x - 15 x + 15 = 0$

Step 1.1.6.2

Subtract $15 x$ from $3 x$ .

$3 x^{2} + 10 x - 8 - 3 x^{2} - 12 x + 15 = 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $3 x^{2} + 10 x - 8 - 3 x^{2} - 12 x + 15$ .

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Step 1.2.1.1

Subtract $3 x^{2}$ from $3 x^{2}$ .

$10 x - 8 + 0 - 12 x + 15 = 0$

Step 1.2.1.2

Add $10 x - 8$ and $0$ .

$10 x - 8 - 12 x + 15 = 0$

Step 1.2.2

Subtract $12 x$ from $10 x$ .

$- 2 x - 8 + 15 = 0$

Step 1.2.3

Add $- 8$ and $15$ .

$- 2 x + 7 = 0$

Step 2

Subtract $7$ from both sides of the equation.

$- 2 x = - 7$

Step 3

Divide each term in $- 2 x = - 7$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 x = - 7$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x = \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

$x = 3 \frac{1}{2}$