Find All Complex Solutions 0.75(x+40)=0.35(x+20)+0.35(x+20)

$0.75 (x + 40) = 0.35 (x + 20) + 0.35 (x + 20)$

Step 1

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

Subtract $0.35 (x + 20)$ from both sides of the equation.

$0.75 (x + 40) - 0.35 (x + 20) = 0.35 (x + 20)$

Subtract $0.35 (x + 20)$ from both sides of the equation.

$0.75 (x + 40) - 0.35 (x + 20) - 0.35 (x + 20) = 0$

Step 2

Simplify $0.75 (x + 40) - 0.35 (x + 20) - 0.35 (x + 20)$ .

Simplify each term.

Apply the distributive property.

$0.75 x + 0.75 \cdot 40 - 0.35 (x + 20) - 0.35 (x + 20) = 0$

Multiply $0.75$ by $40$ .

$0.75 x + 30 - 0.35 (x + 20) - 0.35 (x + 20) = 0$

Apply the distributive property.

$0.75 x + 30 - 0.35 x - 0.35 \cdot 20 - 0.35 (x + 20) = 0$

Multiply $- 0.35$ by $20$ .

$0.75 x + 30 - 0.35 x - 7 - 0.35 (x + 20) = 0$

Apply the distributive property.

$0.75 x + 30 - 0.35 x - 7 - 0.35 x - 0.35 \cdot 20 = 0$

Multiply $- 0.35$ by $20$ .

$0.75 x + 30 - 0.35 x - 7 - 0.35 x - 7 = 0$

Subtract $0.35 x$ from $0.75 x$ .

$0.4 x + 30 - 7 - 0.35 x - 7 = 0$

Subtract $0.35 x$ from $0.4 x$ .

$0.05 x + 30 - 7 - 7 = 0$

Subtract $7$ from $30$ .

$0.05 x + 23 - 7 = 0$

Subtract $7$ from $23$ .

$0.05 x + 16 = 0$

Step 3

Factor $0.05$ out of $0.05 x + 16$ .

Factor $0.05$ out of $0.05 x$ .

$0.05 (x) + 16 = 0$

Factor $0.05$ out of $16$ .

$0.05 x + 0.05 \cdot 320 = 0$

Factor $0.05$ out of $0.05 x + 0.05 \cdot 320$ .

$0.05 (x + 320) = 0$

Step 4

Divide each term in $0.05 (x + 320) = 0$ by $0.05$ and simplify.

Divide each term in $0.05 (x + 320) = 0$ by $0.05$ .

$\frac{0.05 (x + 320)}{0.05} = \frac{0}{0.05}$

Simplify the left side.

Cancel the common factor of $0.05$ .

Cancel the common factor.

$\frac{0.05 (x + 320)}{0.05} = \frac{0}{0.05}$

Divide $x + 320$ by $1$ .

$x + 320 = \frac{0}{0.05}$

Simplify the right side.

Divide $0$ by $0.05$ .

$x + 320 = 0$

Step 5

Subtract $320$ from both sides of the equation.

$x = - 320$

Find All Complex Solutions 0.75(x+40)=0.35(x+20)+0.35(x+20)

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