120=(x-4)(4x-6)

Solution for 120=(x-4)(4x-6) equation:

Simplifying
120 = (x + -4)(4x + -6)

Reorder the terms:
120 = (-4 + x)(4x + -6)

Reorder the terms:
120 = (-4 + x)(-6 + 4x)

Multiply (-4 + x) * (-6 + 4x)
120 = (-4(-6 + 4x) + x(-6 + 4x))
120 = ((-6 * -4 + 4x * -4) + x(-6 + 4x))
120 = ((24 + -16x) + x(-6 + 4x))
120 = (24 + -16x + (-6 * x + 4x * x))
120 = (24 + -16x + (-6x + 4x2))

Combine like terms: -16x + -6x = -22x
120 = (24 + -22x + 4x2)

Solving
120 = 24 + -22x + 4x2

Solving for variable 'x'.

Combine like terms: 120 + -24 = 96
96 + 22x + -4x2 = 24 + -22x + 4x2 + -24 + 22x + -4x2

Reorder the terms:
96 + 22x + -4x2 = 24 + -24 + -22x + 22x + 4x2 + -4x2

Combine like terms: 24 + -24 = 0
96 + 22x + -4x2 = 0 + -22x + 22x + 4x2 + -4x2
96 + 22x + -4x2 = -22x + 22x + 4x2 + -4x2

Combine like terms: -22x + 22x = 0
96 + 22x + -4x2 = 0 + 4x2 + -4x2
96 + 22x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
96 + 22x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + 11x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(48 + 11x + -2x2)' equal to zero and attempt to solve:

Simplifying
48 + 11x + -2x2 = 0

Solving
48 + 11x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-24 + -5.5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -5.5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -5.5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -5.5x + x2 = 0 + 24
-5.5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-5.5x + x2 = 24

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 24 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 24 + 7.5625

Combine like terms: 24 + 7.5625 = 31.5625
7.5625 + -5.5x + x2 = 31.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(x + -2.75) equal to 5.618051264 and -5.618051264.

Subproblem 1
x + -2.75 = 5.618051264

Simplifying
x + -2.75 = 5.618051264

Reorder the terms:
-2.75 + x = 5.618051264

Solving
-2.75 + x = 5.618051264

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 5.618051264 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 5.618051264 + 2.75
x = 5.618051264 + 2.75

Combine like terms: 5.618051264 + 2.75 = 8.368051264
x = 8.368051264

Simplifying
x = 8.368051264

Subproblem 2
x + -2.75 = -5.618051264

Simplifying
x + -2.75 = -5.618051264

Reorder the terms:
-2.75 + x = -5.618051264

Solving
-2.75 + x = -5.618051264

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -5.618051264 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -5.618051264 + 2.75
x = -5.618051264 + 2.75

Combine like terms: -5.618051264 + 2.75 = -2.868051264
x = -2.868051264

Simplifying
x = -2.868051264

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.368051264, -2.868051264}
Solution
x = {8.368051264, -2.868051264}