Find All Complex Solutions 3(x+5)=-4x+8

$3 (x + 5) = - 4 x + 8$

Move all the expressions to the left side of the equation.

Add $4 x$ to both sides of the equation.

$3 (x + 5) + 4 x = 8$

Subtract $8$ from both sides of the equation.

$3 (x + 5) + 4 x - 8 = 0$

Simplify $3 (x + 5) + 4 x - 8$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 5 + 4 x - 8 = 0$

Multiply $3$ by $5$ .

$3 x + 15 + 4 x - 8 = 0$

Add $3 x$ and $4 x$ .

$7 x + 15 - 8 = 0$

Subtract $8$ from $15$ .

$7 x + 7 = 0$

Factor $7$ out of $7 x + 7$ .

Factor $7$ out of $7 x$ .

$7 (x) + 7 = 0$

Factor $7$ out of $7$ .

$7 (x) + 7 (1) = 0$

Factor $7$ out of $7 (x) + 7 (1)$ .

$7 (x + 1) = 0$

Divide each term in $7 (x + 1) = 0$ by $7$ and simplify.

Divide each term in $7 (x + 1) = 0$ by $7$ .

$\frac{7 (x + 1)}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (x + 1)}{7} = \frac{0}{7}$

Divide $x + 1$ by $1$ .

$x + 1 = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$