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.

Subtract $78 x$ from both sides of the equation.

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

Subtract $78 x$ from $58 x$ .

$- 20 x + 52 = - 78$

Step 2

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

Subtract $52$ from both sides of the equation.

$- 20 x = - 78 - 52$

Subtract $52$ from $- 78$ .

$- 20 x = - 130$

Step 3

Divide each term in $- 20 x = - 130$ by $- 20$ and simplify.

Divide each term in $- 20 x = - 130$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 130}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 130}{- 20}$

Divide $x$ by $1$ .

$x = \frac{- 130}{- 20}$

Simplify the right side.

Cancel the common factor of $- 130$ and $- 20$ .

Factor $- 10$ out of $- 130$ .

$x = \frac{- 10 (13)}{- 20}$

Cancel the common factors.

Factor $- 10$ out of $- 20$ .

$x = \frac{- 10 \cdot 13}{- 10 \cdot 2}$

Cancel the common factor.

$x = \frac{- 10 \cdot 13}{- 10 \cdot 2}$

Rewrite the expression.

$x = \frac{13}{2}$