Solve 1/2left(b+3right)left(h+4right)-1/2bh=42

$$\frac{ 1 }{ 2 } \left( b+3 \right) \left( h+4 \right) - \frac{ 1 }{ 2 } bh = 42$$

Solve for b

$$b=-\frac{3h}{4}+18$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by b+3.

$$\left(\frac{1}{2}b+\frac{3}{2}\right)\left(h+4\right)-\frac{1}{2}bh=42$$

Use the distributive property to multiply \frac{1}{2}b+\frac{3}{2} by h+4.

$$\frac{1}{2}bh+2b+\frac{3}{2}h+6-\frac{1}{2}bh=42$$

Combine \frac{1}{2}bh and -\frac{1}{2}bh to get 0.

$$2b+\frac{3}{2}h+6=42$$

Subtract \frac{3}{2}h from both sides.

$$2b+6=42-\frac{3}{2}h$$

Subtract 6 from both sides.

$$2b=42-\frac{3}{2}h-6$$

Subtract 6 from 42 to get 36.

$$2b=36-\frac{3}{2}h$$

The equation is in standard form.

$$2b=-\frac{3h}{2}+36$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{-\frac{3h}{2}+36}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{-\frac{3h}{2}+36}{2}$$

Divide 36-\frac{3h}{2} by 2.

$$b=-\frac{3h}{4}+18$$

Solve for h

$$h=-\frac{4b}{3}+24$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by b+3.

$$\left(\frac{1}{2}b+\frac{3}{2}\right)\left(h+4\right)-\frac{1}{2}bh=42$$

Use the distributive property to multiply \frac{1}{2}b+\frac{3}{2} by h+4.

$$\frac{1}{2}bh+2b+\frac{3}{2}h+6-\frac{1}{2}bh=42$$

Combine \frac{1}{2}bh and -\frac{1}{2}bh to get 0.

$$2b+\frac{3}{2}h+6=42$$

Subtract 2b from both sides.

$$\frac{3}{2}h+6=42-2b$$

Subtract 6 from both sides.

$$\frac{3}{2}h=42-2b-6$$

Subtract 6 from 42 to get 36.

$$\frac{3}{2}h=36-2b$$

Divide both sides of the equation by \frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{2}h}{\frac{3}{2}}=\frac{36-2b}{\frac{3}{2}}$$

Dividing by \frac{3}{2} undoes the multiplication by \frac{3}{2}.

$$h=\frac{36-2b}{\frac{3}{2}}$$

Divide 36-2b by \frac{3}{2} by multiplying 36-2b by the reciprocal of \frac{3}{2}.

$$h=-\frac{4b}{3}+24$$