Solve (-3b-c-10)^2-4(2a-4)=0

$$( - 3 b - c - 10 ) ^ { 2 } - 4 ( 2 a - 4 ) = 0$$

Solve for a

$$a=\frac{\left(3b+c+10\right)^{2}+16}{8}$$

Steps for Solving Linear Equation

Square -3b-c-10.

$$9b^{2}+6bc+60b+c^{2}+20c+100-4\left(2a-4\right)=0$$

Use the distributive property to multiply -4 by 2a-4.

$$9b^{2}+6bc+60b+c^{2}+20c+100-8a+16=0$$

Add 100 and 16 to get 116.

$$9b^{2}+6bc+60b+c^{2}+20c+116-8a=0$$

Subtract 9b^{2} from both sides. Anything subtracted from zero gives its negation.

$$6bc+60b+c^{2}+20c+116-8a=-9b^{2}$$

Subtract 6bc from both sides.

$$60b+c^{2}+20c+116-8a=-9b^{2}-6bc$$

Subtract 60b from both sides.

$$c^{2}+20c+116-8a=-9b^{2}-6bc-60b$$

Subtract c^{2} from both sides.

$$20c+116-8a=-9b^{2}-6bc-60b-c^{2}$$

Subtract 20c from both sides.

$$116-8a=-9b^{2}-6bc-60b-c^{2}-20c$$

Subtract 116 from both sides.

$$-8a=-9b^{2}-6bc-60b-c^{2}-20c-116$$

Divide both sides by -8.

$$\frac{-8a}{-8}=\frac{-\left(3b+c\right)^{2}-20c-60b-116}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$a=\frac{-\left(3b+c\right)^{2}-20c-60b-116}{-8}$$

Divide -60b-20c-116-\left(3b+c\right)^{2} by -8.

$$a=\frac{\left(3b+c\right)^{2}}{8}+\frac{5c}{2}+\frac{15b}{2}+\frac{29}{2}$$

Solve for b (complex solution)

$$b=\frac{-c+2\sqrt{2a-4}-10}{3}$$

$$b=\frac{-c-2\sqrt{2a-4}-10}{3}$$

Solve for b

$$b=\frac{-c+2\sqrt{2a-4}-10}{3}$$

$$b=\frac{-c-2\sqrt{2a-4}-10}{3}\text{, }a\geq 2$$