(4x+4)4x-32=180

Solution for (4x+4)4x-32=180 equation:

(4x+4)4x-32=180

We move all terms to the left:

(4x+4)4x-32-(180)=0

We add all the numbers together, and all the variables

(4x+4)4x-212=0

We multiply parentheses

16x^2+16x-212=0

a = 16; b = 16; c = -212;
Δ = b2-4ac
Δ = 162-4·16·(-212)
Δ = 13824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13824}=\sqrt{2304*6}=\sqrt{2304}*\sqrt{6}=48\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-48\sqrt{6}}{2*16}=\frac{-16-48\sqrt{6}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+48\sqrt{6}}{2*16}=\frac{-16+48\sqrt{6}}{32}
$