Solve for x S=2(ab+ax+bx)

$S = 2 (a b + a x + b x)$

Rewrite the equation as $2 (a b + a x + b x) = S$ .

$2 (a b + a x + b x) = S$

Divide each term in $2 (a b + a x + b x) = S$ by $2$ and simplify.

Divide each term in $2 (a b + a x + b x) = S$ by $2$ .

$\frac{2 (a b + a x + b x)}{2} = \frac{S}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (a b + a x + b x)}{2} = \frac{S}{2}$

Divide $a b + a x + b x$ by $1$ .

$a b + a x + b x = \frac{S}{2}$

Subtract $a b$ from both sides of the equation.

$a x + b x = \frac{S}{2} - a b$

Factor $x$ out of $a x + b x$ .

Factor $x$ out of $a x$ .

$x a + b x = \frac{S}{2} - a b$

Factor $x$ out of $b x$ .

$x a + x b = \frac{S}{2} - a b$

Factor $x$ out of $x a + x b$ .

$x (a + b) = \frac{S}{2} - a b$

Divide each term in $x (a + b) = \frac{S}{2} - a b$ by $a + b$ and simplify.

Divide each term in $x (a + b) = \frac{S}{2} - a b$ by $a + b$ .

$\frac{x (a + b)}{a + b} = \frac{\frac{S}{2}}{a + b} + \frac{- a b}{a + b}$

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

$\frac{x (a + b)}{a + b} = \frac{\frac{S}{2}}{a + b} + \frac{- a b}{a + b}$

Divide $x$ by $1$ .

$x = \frac{\frac{S}{2}}{a + b} + \frac{- a b}{a + b}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{\frac{S}{2} - a b}{a + b}$

Multiply the numerator and denominator of the complex fraction by $2$ .

Multiply $\frac{\frac{S}{2} - a b}{a + b}$ by $\frac{2}{2}$ .

$x = \frac{2}{2} \cdot \frac{\frac{S}{2} - a b}{a + b}$

Combine.

$x = \frac{2 (\frac{S}{2} - a b)}{2 (a + b)}$

Apply the distributive property.

$x = \frac{2 \frac{S}{2} + 2 (- a b)}{2 a + 2 b}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \frac{2 \frac{S}{2} + 2 (- a b)}{2 a + 2 b}$

Rewrite the expression.

$x = \frac{S + 2 (- a b)}{2 a + 2 b}$

Multiply $- 1$ by $2$ .

$x = \frac{S - 2 a b}{2 a + 2 b}$

Factor $2$ out of $2 a + 2 b$ .

Factor $2$ out of $2 a$ .

$x = \frac{S - 2 a b}{2 (a) + 2 b}$

Factor $2$ out of $2 b$ .

$x = \frac{S - 2 a b}{2 (a) + 2 (b)}$

Factor $2$ out of $2 (a) + 2 (b)$ .

$x = \frac{S - 2 a b}{2 (a + b)}$

Solve for x S=2(ab+ax+bx)

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