Solve for c a=1/2*((b+c)h)

$a = \frac{1}{2} \cdot ((b + c) h)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot ((b + c) h) = a$ .

$\frac{1}{2} \cdot ((b + c) h) = a$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot ((b + c) h)) = 2 a$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot ((b + c) h))$ .

Apply the distributive property.

$2 (\frac{1}{2} \cdot (b h + c h)) = 2 a$

Apply the distributive property.

$2 (\frac{1}{2} (b h) + \frac{1}{2} (c h)) = 2 a$

Multiply $\frac{1}{2} (b h)$ .

Combine $b$ and $\frac{1}{2}$ .

$2 (\frac{b}{2} h + \frac{1}{2} (c h)) = 2 a$

Combine $\frac{b}{2}$ and $h$ .

$2 (\frac{b h}{2} + \frac{1}{2} (c h)) = 2 a$

$2 (\frac{b h}{2} + \frac{1}{2} (c h)) = 2 a$

Multiply $\frac{1}{2} (c h)$ .

Combine $c$ and $\frac{1}{2}$ .

$2 (\frac{b h}{2} + \frac{c}{2} h) = 2 a$

Combine $\frac{c}{2}$ and $h$ .

$2 (\frac{b h}{2} + \frac{c h}{2}) = 2 a$

$2 (\frac{b h}{2} + \frac{c h}{2}) = 2 a$

Apply the distributive property.

$2 \frac{b h}{2} + 2 \frac{c h}{2} = 2 a$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{b h}{2} + 2 \frac{c h}{2} = 2 a$

Rewrite the expression.

$b h + 2 \frac{c h}{2} = 2 a$

$b h + 2 \frac{c h}{2} = 2 a$

Cancel the common factor of $2$ .

Cancel the common factor.

$b h + 2 \frac{c h}{2} = 2 a$

Rewrite the expression.

$b h + c h = 2 a$

$b h + c h = 2 a$

$b h + c h = 2 a$

$b h + c h = 2 a$

Step 4

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

$c h = 2 a - b h$

Step 5

Divide each term in $c h = 2 a - b h$ by $h$ and simplify.

Divide each term in $c h = 2 a - b h$ by $h$ .

$\frac{c h}{h} = \frac{2 a}{h} + \frac{- b h}{h}$

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{c h}{h} = \frac{2 a}{h} + \frac{- b h}{h}$

Divide $c$ by $1$ .

$c = \frac{2 a}{h} + \frac{- b h}{h}$

$c = \frac{2 a}{h} + \frac{- b h}{h}$

$c = \frac{2 a}{h} + \frac{- b h}{h}$

Simplify the right side.

Cancel the common factor of $h$ .

Cancel the common factor.

$c = \frac{2 a}{h} + \frac{- b h}{h}$

Divide $- b$ by $1$ .

$c = \frac{2 a}{h} - b$

$c = \frac{2 a}{h} - b$

$c = \frac{2 a}{h} - b$

$c = \frac{2 a}{h} - b$

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