Solve for x 2(7(x+3)-8)=54

$2 (7 (x + 3) - 8) = 54$

Step 1

Divide each term in $2 (7 (x + 3) - 8) = 54$ by $2$ and simplify.

Divide each term in $2 (7 (x + 3) - 8) = 54$ by $2$ .

$\frac{2 (7 (x + 3) - 8)}{2} = \frac{54}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (7 (x + 3) - 8)}{2} = \frac{54}{2}$

Divide $7 (x + 3) - 8$ by $1$ .

$7 (x + 3) - 8 = \frac{54}{2}$

Simplify each term.

Apply the distributive property.

$7 x + 7 \cdot 3 - 8 = \frac{54}{2}$

Multiply $7$ by $3$ .

$7 x + 21 - 8 = \frac{54}{2}$

Subtract $8$ from $21$ .

$7 x + 13 = \frac{54}{2}$

Simplify the right side.

Divide $54$ by $2$ .

$7 x + 13 = 27$

Step 2

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

Subtract $13$ from both sides of the equation.

$7 x = 27 - 13$

Subtract $13$ from $27$ .

$7 x = 14$

Step 3

Divide each term in $7 x = 14$ by $7$ and simplify.

Divide each term in $7 x = 14$ by $7$ .

$\frac{7 x}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{14}{7}$

Divide $x$ by $1$ .

$x = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x = 2$