Solve for x 8/9(54x-36)+2=-3/4(-40+16x)+90x

$\frac{8}{9} (54 x - 36) + 2 = - \frac{3}{4} (- 40 + 16 x) + 90 x$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{3}{4} \cdot (- 40 + 16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Simplify $- \frac{3}{4} \cdot (- 40 + 16 x) + 90 x$ .

Simplify each term.

Apply the distributive property.

$- \frac{3}{4} \cdot - 40 - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot - 40 - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Factor $4$ out of $- 40$ .

$\frac{- 3}{4} \cdot (4 (- 10)) - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Cancel the common factor.

$\frac{- 3}{4} \cdot (4 \cdot - 10) - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Rewrite the expression.

$- 3 \cdot - 10 - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Multiply $- 3$ by $- 10$ .

$30 - \frac{3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$30 + \frac{- 3}{4} (16 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Factor $4$ out of $16 x$ .

$30 + \frac{- 3}{4} (4 (4 x)) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Cancel the common factor.

$30 + \frac{- 3}{4} (4 (4 x)) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Rewrite the expression.

$30 - 3 (4 x) + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Multiply $4$ by $- 3$ .

$30 - 12 x + 90 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Add $- 12 x$ and $90 x$ .

$30 + 78 x = \frac{8}{9} \cdot (54 x - 36) + 2$

Simplify $\frac{8}{9} \cdot (54 x - 36) + 2$ .

Simplify each term.

Apply the distributive property.

$30 + 78 x = \frac{8}{9} (54 x) + \frac{8}{9} \cdot - 36 + 2$

Cancel the common factor of $9$ .

Factor $9$ out of $54 x$ .

$30 + 78 x = \frac{8}{9} (9 (6 x)) + \frac{8}{9} \cdot - 36 + 2$

Cancel the common factor.

$30 + 78 x = \frac{8}{9} (9 (6 x)) + \frac{8}{9} \cdot - 36 + 2$

Rewrite the expression.

$30 + 78 x = 8 (6 x) + \frac{8}{9} \cdot - 36 + 2$

Multiply $6$ by $8$ .

$30 + 78 x = 48 x + \frac{8}{9} \cdot - 36 + 2$

Cancel the common factor of $9$ .

Factor $9$ out of $- 36$ .

$30 + 78 x = 48 x + \frac{8}{9} \cdot (9 (- 4)) + 2$

Cancel the common factor.

$30 + 78 x = 48 x + \frac{8}{9} \cdot (9 \cdot - 4) + 2$

Rewrite the expression.

$30 + 78 x = 48 x + 8 \cdot - 4 + 2$

Multiply $8$ by $- 4$ .

$30 + 78 x = 48 x - 32 + 2$

Add $- 32$ and $2$ .

$30 + 78 x = 48 x - 30$

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

Subtract $48 x$ from both sides of the equation.

$30 + 78 x - 48 x = - 30$

Subtract $48 x$ from $78 x$ .

$30 + 30 x = - 30$

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

Subtract $30$ from both sides of the equation.

$30 x = - 30 - 30$

Subtract $30$ from $- 30$ .

$30 x = - 60$

Divide each term in $30 x = - 60$ by $30$ and simplify.

Divide each term in $30 x = - 60$ by $30$ .

$\frac{30 x}{30} = \frac{- 60}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 x}{30} = \frac{- 60}{30}$

Divide $x$ by $1$ .

$x = \frac{- 60}{30}$

Simplify the right side.

Divide $- 60$ by $30$ .

$x = - 2$

Solve for x 8/9(54x-36)+2=-3/4(-40+16x)+90x

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