4*(x+5)*-4*(3x-2)=90

Solution for 4*(x+5)*-4*(3x-2)=90 equation:

Simplifying
4(x + 5) * -4(3x + -2) = 90

Reorder the terms:
4(5 + x) * -4(3x + -2) = 90

Reorder the terms:
4(5 + x) * -4(-2 + 3x) = 90

Reorder the terms for easier multiplication:
4 * -4(5 + x)(-2 + 3x) = 90

Multiply 4 * -4
-16(5 + x)(-2 + 3x) = 90

Multiply (5 + x) * (-2 + 3x)
-16(5(-2 + 3x) + x(-2 + 3x)) = 90
-16((-2 * 5 + 3x * 5) + x(-2 + 3x)) = 90
-16((-10 + 15x) + x(-2 + 3x)) = 90
-16(-10 + 15x + (-2 * x + 3x * x)) = 90
-16(-10 + 15x + (-2x + 3x2)) = 90

Combine like terms: 15x + -2x = 13x
-16(-10 + 13x + 3x2) = 90
(-10 * -16 + 13x * -16 + 3x2 * -16) = 90
(160 + -208x + -48x2) = 90

Solving
160 + -208x + -48x2 = 90

Solving for variable 'x'.

Reorder the terms:
160 + -90 + -208x + -48x2 = 90 + -90

Combine like terms: 160 + -90 = 70
70 + -208x + -48x2 = 90 + -90

Combine like terms: 90 + -90 = 0
70 + -208x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -104x + -24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(35 + -104x + -24x2)' equal to zero and attempt to solve:

Simplifying
35 + -104x + -24x2 = 0

Solving
35 + -104x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-1.458333333 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '1.458333333' to each side of the equation.
-1.458333333 + 4.333333333x + 1.458333333 + x2 = 0 + 1.458333333

Reorder the terms:
-1.458333333 + 1.458333333 + 4.333333333x + x2 = 0 + 1.458333333

Combine like terms: -1.458333333 + 1.458333333 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 1.458333333
4.333333333x + x2 = 0 + 1.458333333

Combine like terms: 0 + 1.458333333 = 1.458333333
4.333333333x + x2 = 1.458333333

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 1.458333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 1.458333333 + 4.694444446

Combine like terms: 1.458333333 + 4.694444446 = 6.152777779
4.694444446 + 4.333333333x + x2 = 6.152777779

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 6.152777779

Calculate the square root of the right side: 2.480479345

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.480479345 and -2.480479345.

Subproblem 1
x + 2.166666667 = 2.480479345

Simplifying
x + 2.166666667 = 2.480479345

Reorder the terms:
2.166666667 + x = 2.480479345

Solving
2.166666667 + x = 2.480479345

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 2.480479345 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 2.480479345 + -2.166666667
x = 2.480479345 + -2.166666667

Combine like terms: 2.480479345 + -2.166666667 = 0.313812678
x = 0.313812678

Simplifying
x = 0.313812678

Subproblem 2
x + 2.166666667 = -2.480479345

Simplifying
x + 2.166666667 = -2.480479345

Reorder the terms:
2.166666667 + x = -2.480479345

Solving
2.166666667 + x = -2.480479345

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -2.480479345 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -2.480479345 + -2.166666667
x = -2.480479345 + -2.166666667

Combine like terms: -2.480479345 + -2.166666667 = -4.647146012
x = -4.647146012

Simplifying
x = -4.647146012

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.313812678, -4.647146012}
Solution
x = {0.313812678, -4.647146012}