Solve for x 14x-12(4x+6)=3(x-4)-18

$14 x - 12 (4 x + 6) = 3 (x - 4) - 18$

Step 1

Simplify $14 x - 12 (4 x + 6)$ .

Simplify each term.

Apply the distributive property.

$14 x - 12 (4 x) - 12 \cdot 6 = 3 (x - 4) - 18$

Multiply $4$ by $- 12$ .

$14 x - 48 x - 12 \cdot 6 = 3 (x - 4) - 18$

Multiply $- 12$ by $6$ .

$14 x - 48 x - 72 = 3 (x - 4) - 18$

Subtract $48 x$ from $14 x$ .

$- 34 x - 72 = 3 (x - 4) - 18$

Step 2

Simplify $3 (x - 4) - 18$ .

Simplify each term.

Apply the distributive property.

$- 34 x - 72 = 3 x + 3 \cdot - 4 - 18$

Multiply $3$ by $- 4$ .

$- 34 x - 72 = 3 x - 12 - 18$

Subtract $18$ from $- 12$ .

$- 34 x - 72 = 3 x - 30$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$- 34 x - 72 - 3 x = - 30$

Subtract $3 x$ from $- 34 x$ .

$- 37 x - 72 = - 30$

Step 4

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

Add $72$ to both sides of the equation.

$- 37 x = - 30 + 72$

Add $- 30$ and $72$ .

$- 37 x = 42$

Step 5

Divide each term in $- 37 x = 42$ by $- 37$ and simplify.

Divide each term in $- 37 x = 42$ by $- 37$ .

$\frac{- 37 x}{- 37} = \frac{42}{- 37}$

Simplify the left side.

Cancel the common factor of $- 37$ .

Cancel the common factor.

$\frac{- 37 x}{- 37} = \frac{42}{- 37}$

Divide $x$ by $1$ .

$x = \frac{42}{- 37}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{42}{37}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{42}{37}$

Decimal Form:

$x = - 1.\overline{135}$

Mixed Number Form:

$x = - 1 \frac{5}{37}$

Solve for x 14x-12(4x+6)=3(x-4)-18

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