40x^2+264x-144=0

Solution for 40x^2+264x-144=0 equation:

Simplifying
40x2 + 264x + -144 = 0

Reorder the terms:
-144 + 264x + 40x2 = 0

Solving
-144 + 264x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-18 + 33x + 5x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-18 + 33x + 5x2)' equal to zero and attempt to solve:

Simplifying
-18 + 33x + 5x2 = 0

Solving
-18 + 33x + 5x2 = 0

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

Divide each side by '5'.
-3.6 + 6.6x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 6.6x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 6.6x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 6.6x + x2 = 0 + 3.6
6.6x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
6.6x + x2 = 3.6

The x term is 6.6x.  Take half its coefficient (3.3).
Square it (10.89) and add it to both sides.

Add '10.89' to each side of the equation.
6.6x + 10.89 + x2 = 3.6 + 10.89

Reorder the terms:
10.89 + 6.6x + x2 = 3.6 + 10.89

Combine like terms: 3.6 + 10.89 = 14.49
10.89 + 6.6x + x2 = 14.49

Factor a perfect square on the left side:
(x + 3.3)(x + 3.3) = 14.49

Calculate the square root of the right side: 3.806573262

Break this problem into two subproblems by setting 
(x + 3.3) equal to 3.806573262 and -3.806573262.

Subproblem 1
x + 3.3 = 3.806573262

Simplifying
x + 3.3 = 3.806573262

Reorder the terms:
3.3 + x = 3.806573262

Solving
3.3 + x = 3.806573262

Solving for variable 'x'.

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

Add '-3.3' to each side of the equation.
3.3 + -3.3 + x = 3.806573262 + -3.3

Combine like terms: 3.3 + -3.3 = 0.0
0.0 + x = 3.806573262 + -3.3
x = 3.806573262 + -3.3

Combine like terms: 3.806573262 + -3.3 = 0.506573262
x = 0.506573262

Simplifying
x = 0.506573262

Subproblem 2
x + 3.3 = -3.806573262

Simplifying
x + 3.3 = -3.806573262

Reorder the terms:
3.3 + x = -3.806573262

Solving
3.3 + x = -3.806573262

Solving for variable 'x'.

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

Add '-3.3' to each side of the equation.
3.3 + -3.3 + x = -3.806573262 + -3.3

Combine like terms: 3.3 + -3.3 = 0.0
0.0 + x = -3.806573262 + -3.3
x = -3.806573262 + -3.3

Combine like terms: -3.806573262 + -3.3 = -7.106573262
x = -7.106573262

Simplifying
x = -7.106573262

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.506573262, -7.106573262}
Solution
x = {0.506573262, -7.106573262}