Solve A=4*(a^2+3b)+a^2+4b

$$A = 4 \cdot ( a ^ { 2 } + 3 b ) + a ^ { 2 } + 4 b$$

Solve for A

$$A=5a^{2}+16b$$

Solution Steps

Use the distributive property to multiply 4 by a^{2}+3b.

$$A=4a^{2}+12b+a^{2}+4b$$

Combine 4a^{2} and a^{2} to get 5a^{2}.

$$A=5a^{2}+12b+4b$$

Combine 12b and 4b to get 16b.

$$A=5a^{2}+16b$$

Solve for a

$$a=\frac{\sqrt{5\left(A-16b\right)}}{5}$$

$$a=-\frac{\sqrt{5\left(A-16b\right)}}{5}\text{, }A\geq 16b$$