(4x+6)*(x-7)=132

Solution for (4x+6)*(x-7)=132 equation:

Simplifying
(4x + 6)(x + -7) = 132

Reorder the terms:
(6 + 4x)(x + -7) = 132

Reorder the terms:
(6 + 4x)(-7 + x) = 132

Multiply (6 + 4x) * (-7 + x)
(6(-7 + x) + 4x * (-7 + x)) = 132
((-7 * 6 + x * 6) + 4x * (-7 + x)) = 132
((-42 + 6x) + 4x * (-7 + x)) = 132
(-42 + 6x + (-7 * 4x + x * 4x)) = 132
(-42 + 6x + (-28x + 4x2)) = 132

Combine like terms: 6x + -28x = -22x
(-42 + -22x + 4x2) = 132

Solving
-42 + -22x + 4x2 = 132

Solving for variable 'x'.

Reorder the terms:
-42 + -132 + -22x + 4x2 = 132 + -132

Combine like terms: -42 + -132 = -174
-174 + -22x + 4x2 = 132 + -132

Combine like terms: 132 + -132 = 0
-174 + -22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-87 + -11x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-87 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-87 + -11x + 2x2 = 0

Solving
-87 + -11x + 2x2 = 0

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

Divide each side by '2'.
-43.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '43.5' to each side of the equation.
-43.5 + -5.5x + 43.5 + x2 = 0 + 43.5

Reorder the terms:
-43.5 + 43.5 + -5.5x + x2 = 0 + 43.5

Combine like terms: -43.5 + 43.5 = 0.0
0.0 + -5.5x + x2 = 0 + 43.5
-5.5x + x2 = 0 + 43.5

Combine like terms: 0 + 43.5 = 43.5
-5.5x + x2 = 43.5

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 = 43.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 43.5 + 7.5625

Combine like terms: 43.5 + 7.5625 = 51.0625
7.5625 + -5.5x + x2 = 51.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 51.0625

Calculate the square root of the right side: 7.145802964

Break this problem into two subproblems by setting 
(x + -2.75) equal to 7.145802964 and -7.145802964.

Subproblem 1
x + -2.75 = 7.145802964

Simplifying
x + -2.75 = 7.145802964

Reorder the terms:
-2.75 + x = 7.145802964

Solving
-2.75 + x = 7.145802964

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 = 7.145802964 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 7.145802964 + 2.75
x = 7.145802964 + 2.75

Combine like terms: 7.145802964 + 2.75 = 9.895802964
x = 9.895802964

Simplifying
x = 9.895802964

Subproblem 2
x + -2.75 = -7.145802964

Simplifying
x + -2.75 = -7.145802964

Reorder the terms:
-2.75 + x = -7.145802964

Solving
-2.75 + x = -7.145802964

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 = -7.145802964 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -7.145802964 + 2.75
x = -7.145802964 + 2.75

Combine like terms: -7.145802964 + 2.75 = -4.395802964
x = -4.395802964

Simplifying
x = -4.395802964

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.895802964, -4.395802964}
Solution
x = {9.895802964, -4.395802964}