(4x+2)(x-6)=8

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Solution for (4x+2)(x-6)=8 equation: 


Simplifying
(4x + 2)(x + -6) = 8

Reorder the terms:
(2 + 4x)(x + -6) = 8

Reorder the terms:
(2 + 4x)(-6 + x) = 8

Multiply (2 + 4x) * (-6 + x)
(2(-6 + x) + 4x * (-6 + x)) = 8
((-6 * 2 + x * 2) + 4x * (-6 + x)) = 8
((-12 + 2x) + 4x * (-6 + x)) = 8
(-12 + 2x + (-6 * 4x + x * 4x)) = 8
(-12 + 2x + (-24x + 4x2)) = 8

Combine like terms: 2x + -24x = -22x
(-12 + -22x + 4x2) = 8

Solving
-12 + -22x + 4x2 = 8

Solving for variable 'x'.

Reorder the terms:
-12 + -8 + -22x + 4x2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + -22x + 4x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + -22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-10 + -11x + 2x2 = 0

Solving
-10 + -11x + 2x2 = 0

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

Divide each side by '2'.
-5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -5.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -5.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -5.5x + x2 = 0 + 5
-5.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-5.5x + x2 = 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 = 5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 5 + 7.5625

Combine like terms: 5 + 7.5625 = 12.5625
7.5625 + -5.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.54436172 and -3.54436172.


Subproblem 1
x + -2.75 = 3.54436172

Simplifying
x + -2.75 = 3.54436172

Reorder the terms:
-2.75 + x = 3.54436172

Solving
-2.75 + x = 3.54436172

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 = 3.54436172 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 3.54436172 + 2.75
x = 3.54436172 + 2.75

Combine like terms: 3.54436172 + 2.75 = 6.29436172
x = 6.29436172

Simplifying
x = 6.29436172


Subproblem 2
x + -2.75 = -3.54436172

Simplifying
x + -2.75 = -3.54436172

Reorder the terms:
-2.75 + x = -3.54436172

Solving
-2.75 + x = -3.54436172

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 = -3.54436172 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -3.54436172 + 2.75
x = -3.54436172 + 2.75

Combine like terms: -3.54436172 + 2.75 = -0.79436172
x = -0.79436172

Simplifying
x = -0.79436172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.29436172, -0.79436172}
Solution
x = {6.29436172, -0.79436172}

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