Find All Complex Solutions 58x+52=-78x-78

$58 x + 52 = - 78 x - 78$

Step 1

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

Add $78 x$ to both sides of the equation.

$58 x + 52 + 78 x = - 78$

Add $58 x$ and $78 x$ .

$136 x + 52 = - 78$

Step 2

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

Subtract $52$ from both sides of the equation.

$136 x = - 78 - 52$

Subtract $52$ from $- 78$ .

$136 x = - 130$

Step 3

Divide each term in $136 x = - 130$ by $136$ and simplify.

Divide each term in $136 x = - 130$ by $136$ .

$\frac{136 x}{136} = \frac{- 130}{136}$

Simplify the left side.

Cancel the common factor of $136$ .

Cancel the common factor.

$\frac{136 x}{136} = \frac{- 130}{136}$

Divide $x$ by $1$ .

$x = \frac{- 130}{136}$

Simplify the right side.

Cancel the common factor of $- 130$ and $136$ .

Factor $2$ out of $- 130$ .

$x = \frac{2 (- 65)}{136}$

Cancel the common factors.

Factor $2$ out of $136$ .

$x = \frac{2 \cdot - 65}{2 \cdot 68}$

Cancel the common factor.

$x = \frac{2 \cdot - 65}{2 \cdot 68}$

Rewrite the expression.

$x = \frac{- 65}{68}$

Move the negative in front of the fraction.

$x = - \frac{65}{68}$