Solve 4w^2+w(9-2w)+w(12-2w)-48=0

$$4 w ^ { 2 } + w ( 9 - 2 w ) + w ( 12 - 2 w ) - 48 = 0$$

Solve for w

$$w = \frac{16}{7} = 2\frac{2}{7} \approx 2.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply w by 9-2w.

$$4w^{2}+9w-2w^{2}+w\left(12-2w\right)-48=0$$

Combine 4w^{2} and -2w^{2} to get 2w^{2}.

$$2w^{2}+9w+w\left(12-2w\right)-48=0$$

Use the distributive property to multiply w by 12-2w.

$$2w^{2}+9w+12w-2w^{2}-48=0$$

Combine 9w and 12w to get 21w.

$$2w^{2}+21w-2w^{2}-48=0$$

Combine 2w^{2} and -2w^{2} to get 0.

$$21w-48=0$$

Add 48 to both sides. Anything plus zero gives itself.

$$21w=48$$

Divide both sides by 21.

$$w=\frac{48}{21}$$

Reduce the fraction \frac{48}{21} to lowest terms by extracting and canceling out 3.

$$w=\frac{16}{7}$$