Algebra Examples

$2 x (7 x + 6) - 7 x (2 x - 4) = - 160$

Step 1

Simplify $2 x (7 x + 6) - 7 x (2 x - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x (7 x) + 2 x \cdot 6 - 7 x (2 x - 4) = - 160$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 \cdot 7 x \cdot x + 2 x \cdot 6 - 7 x (2 x - 4) = - 160$

Step 1.1.3

Multiply $6$ by $2$ .

$2 \cdot 7 x \cdot x + 12 x - 7 x (2 x - 4) = - 160$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

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Step 1.1.4.1.1

Move $x$ .

$2 \cdot 7 (x \cdot x) + 12 x - 7 x (2 x - 4) = - 160$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$2 \cdot 7 x^{2} + 12 x - 7 x (2 x - 4) = - 160$

Step 1.1.4.2

Multiply $2$ by $7$ .

$14 x^{2} + 12 x - 7 x (2 x - 4) = - 160$

Step 1.1.5

Apply the distributive property.

$14 x^{2} + 12 x - 7 x (2 x) - 7 x \cdot - 4 = - 160$

Step 1.1.6

Rewrite using the commutative property of multiplication.

$14 x^{2} + 12 x - 7 \cdot 2 x \cdot x - 7 x \cdot - 4 = - 160$

Step 1.1.7

Multiply $- 4$ by $- 7$ .

$14 x^{2} + 12 x - 7 \cdot 2 x \cdot x + 28 x = - 160$

Step 1.1.8

Simplify each term.

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Step 1.1.8.1

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

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Step 1.1.8.1.1

Move $x$ .

$14 x^{2} + 12 x - 7 \cdot 2 (x \cdot x) + 28 x = - 160$

Step 1.1.8.1.2

Multiply $x$ by $x$ .

$14 x^{2} + 12 x - 7 \cdot 2 x^{2} + 28 x = - 160$

Step 1.1.8.2

Multiply $- 7$ by $2$ .

$14 x^{2} + 12 x - 14 x^{2} + 28 x = - 160$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $14 x^{2} + 12 x - 14 x^{2} + 28 x$ .

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Step 1.2.1.1

Subtract $14 x^{2}$ from $14 x^{2}$ .

$12 x + 0 + 28 x = - 160$

Step 1.2.1.2

Add $12 x$ and $0$ .

$12 x + 28 x = - 160$

Step 1.2.2

Add $12 x$ and $28 x$ .

$40 x = - 160$

Step 2

Divide each term in $40 x = - 160$ by $40$ and simplify.

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Step 2.1

Divide each term in $40 x = - 160$ by $40$ .

$\frac{40 x}{40} = \frac{- 160}{40}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $40$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{40 x}{40} = \frac{- 160}{40}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 160}{40}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 160$ by $40$ .

$x = - 4$