Find All Complex Solutions 7(5x+9)=18-(x+9)

$7 (5 x + 9) = 18 - (x + 9)$

Step 1

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

Subtract $18$ from both sides of the equation.

$7 (5 x + 9) - 18 = - (x + 9)$

Add $x + 9$ to both sides of the equation.

$7 (5 x + 9) - 18 + x + 9 = 0$

Step 2

Simplify $7 (5 x + 9) - 18 + x + 9$ .

Simplify each term.

Apply the distributive property.

$7 (5 x) + 7 \cdot 9 - 18 + x + 9 = 0$

Multiply $5$ by $7$ .

$35 x + 7 \cdot 9 - 18 + x + 9 = 0$

Multiply $7$ by $9$ .

$35 x + 63 - 18 + x + 9 = 0$

Add $35 x$ and $x$ .

$36 x + 63 - 18 + 9 = 0$

Subtract $18$ from $63$ .

$36 x + 45 + 9 = 0$

Add $45$ and $9$ .

$36 x + 54 = 0$

Step 3

Factor $18$ out of $36 x + 54$ .

Factor $18$ out of $36 x$ .

$18 (2 x) + 54 = 0$

Factor $18$ out of $54$ .

$18 (2 x) + 18 (3) = 0$

Factor $18$ out of $18 (2 x) + 18 (3)$ .

$18 (2 x + 3) = 0$

Step 4

Divide each term in $18 (2 x + 3) = 0$ by $18$ and simplify.

Divide each term in $18 (2 x + 3) = 0$ by $18$ .

$\frac{18 (2 x + 3)}{18} = \frac{0}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 (2 x + 3)}{18} = \frac{0}{18}$

Divide $2 x + 3$ by $1$ .

$2 x + 3 = \frac{0}{18}$

Simplify the right side.

Divide $0$ by $18$ .

$2 x + 3 = 0$

Step 5

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Step 6

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Find All Complex Solutions 7(5x+9)=18-(x+9)

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