Solve for x 3/2(x+3/5)=-3/5

$\frac{3}{2} (x + \frac{3}{5}) = - \frac{3}{5}$

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} \cdot (x + \frac{3}{5})) = \frac{2}{3} (- \frac{3}{5})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} (\frac{3}{2} \cdot (x + \frac{3}{5}))$ .

Apply the distributive property.

$\frac{2}{3} (\frac{3}{2} x + \frac{3}{2} \cdot \frac{3}{5}) = \frac{2}{3} (- \frac{3}{5})$

Combine $\frac{3}{2}$ and $x$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot \frac{3}{5}) = \frac{2}{3} (- \frac{3}{5})$

Multiply $\frac{3}{2} \cdot \frac{3}{5}$ .

Multiply $\frac{3}{2}$ by $\frac{3}{5}$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{3 \cdot 3}{2 \cdot 5}) = \frac{2}{3} (- \frac{3}{5})$

Multiply $3$ by $3$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{9}{2 \cdot 5}) = \frac{2}{3} (- \frac{3}{5})$

Multiply $2$ by $5$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{9}{10}) = \frac{2}{3} (- \frac{3}{5})$

Apply the distributive property.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Rewrite the expression.

$x + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$x + \frac{2}{3} \cdot \frac{9}{2 (5)} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor.

$x + \frac{2}{3} \cdot \frac{9}{2 \cdot 5} = \frac{2}{3} (- \frac{3}{5})$

Rewrite the expression.

$x + \frac{1}{3} \cdot \frac{9}{5} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x + \frac{1}{3} \cdot \frac{3 (3)}{5} = \frac{2}{3} (- \frac{3}{5})$

Cancel the common factor.

$x + \frac{1}{3} \cdot \frac{3 \cdot 3}{5} = \frac{2}{3} (- \frac{3}{5})$

Rewrite the expression.

$x + \frac{3}{5} = \frac{2}{3} (- \frac{3}{5})$

Simplify the right side.

Simplify $\frac{2}{3} (- \frac{3}{5})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x + \frac{3}{5} = \frac{2}{3} \cdot \frac{- 3}{5}$

Factor $3$ out of $- 3$ .

$x + \frac{3}{5} = \frac{2}{3} \cdot \frac{3 (- 1)}{5}$

Cancel the common factor.

$x + \frac{3}{5} = \frac{2}{3} \cdot \frac{3 \cdot - 1}{5}$

Rewrite the expression.

$x + \frac{3}{5} = 2 (\frac{- 1}{5})$

Combine $2$ and $\frac{- 1}{5}$ .

$x + \frac{3}{5} = \frac{2 \cdot - 1}{5}$

Simplify the expression.

Multiply $2$ by $- 1$ .

$x + \frac{3}{5} = \frac{- 2}{5}$

Move the negative in front of the fraction.

$x + \frac{3}{5} = - \frac{2}{5}$

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

Subtract $\frac{3}{5}$ from both sides of the equation.

$x = - \frac{2}{5} - \frac{3}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 2 - 3}{5}$

Subtract $3$ from $- 2$ .

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

Divide $- 5$ by $5$ .

$x = - 1$

Solve for x 3/2(x+3/5)=-3/5

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