Algebra Examples

$- 12 = 5 (6 x + 4) + 7 (x + 6)$

Step 1

Rewrite the equation as $5 (6 x + 4) + 7 (x + 6) = - 12$ .

$5 (6 x + 4) + 7 (x + 6) = - 12$

Step 2

Simplify $5 (6 x + 4) + 7 (x + 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$5 (6 x) + 5 \cdot 4 + 7 (x + 6) = - 12$

Step 2.1.2

Multiply $6$ by $5$ .

$30 x + 5 \cdot 4 + 7 (x + 6) = - 12$

Step 2.1.3

Multiply $5$ by $4$ .

$30 x + 20 + 7 (x + 6) = - 12$

Step 2.1.4

Apply the distributive property.

$30 x + 20 + 7 x + 7 \cdot 6 = - 12$

Step 2.1.5

Multiply $7$ by $6$ .

$30 x + 20 + 7 x + 42 = - 12$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $30 x$ and $7 x$ .

$37 x + 20 + 42 = - 12$

Step 2.2.2

Add $20$ and $42$ .

$37 x + 62 = - 12$

Step 3

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

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Step 3.1

Subtract $62$ from both sides of the equation.

$37 x = - 12 - 62$

Step 3.2

Subtract $62$ from $- 12$ .

$37 x = - 74$

Step 4

Divide each term in $37 x = - 74$ by $37$ and simplify.

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Step 4.1

Divide each term in $37 x = - 74$ by $37$ .

$\frac{37 x}{37} = \frac{- 74}{37}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $37$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{37 x}{37} = \frac{- 74}{37}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 74}{37}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 74$ by $37$ .

$x = - 2$