4(x+2)(6x-9)=20

Solution for 4(x+2)(6x-9)=20 equation:

Simplifying
4(x + 2)(6x + -9) = 20

Reorder the terms:
4(2 + x)(6x + -9) = 20

Reorder the terms:
4(2 + x)(-9 + 6x) = 20

Multiply (2 + x) * (-9 + 6x)
4(2(-9 + 6x) + x(-9 + 6x)) = 20
4((-9 * 2 + 6x * 2) + x(-9 + 6x)) = 20
4((-18 + 12x) + x(-9 + 6x)) = 20
4(-18 + 12x + (-9 * x + 6x * x)) = 20
4(-18 + 12x + (-9x + 6x2)) = 20

Combine like terms: 12x + -9x = 3x
4(-18 + 3x + 6x2) = 20
(-18 * 4 + 3x * 4 + 6x2 * 4) = 20
(-72 + 12x + 24x2) = 20

Solving
-72 + 12x + 24x2 = 20

Solving for variable 'x'.

Reorder the terms:
-72 + -20 + 12x + 24x2 = 20 + -20

Combine like terms: -72 + -20 = -92
-92 + 12x + 24x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-92 + 12x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + 3x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + 3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-23 + 3x + 6x2 = 0

Solving
-23 + 3x + 6x2 = 0

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

Divide each side by '6'.
-3.833333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + 0.5x + 3.833333333 + x2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + 0.5x + x2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + 3.833333333
0.5x + x2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
0.5x + x2 = 3.833333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.833333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.833333333 + 0.0625

Combine like terms: 3.833333333 + 0.0625 = 3.895833333
0.0625 + 0.5x + x2 = 3.895833333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.895833333

Calculate the square root of the right side: 1.973786547

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.973786547 and -1.973786547.

Subproblem 1
x + 0.25 = 1.973786547

Simplifying
x + 0.25 = 1.973786547

Reorder the terms:
0.25 + x = 1.973786547

Solving
0.25 + x = 1.973786547

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.973786547 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.973786547 + -0.25
x = 1.973786547 + -0.25

Combine like terms: 1.973786547 + -0.25 = 1.723786547
x = 1.723786547

Simplifying
x = 1.723786547

Subproblem 2
x + 0.25 = -1.973786547

Simplifying
x + 0.25 = -1.973786547

Reorder the terms:
0.25 + x = -1.973786547

Solving
0.25 + x = -1.973786547

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.973786547 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.973786547 + -0.25
x = -1.973786547 + -0.25

Combine like terms: -1.973786547 + -0.25 = -2.223786547
x = -2.223786547

Simplifying
x = -2.223786547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.723786547, -2.223786547}
Solution
x = {1.723786547, -2.223786547}