4(x^2-6x+9)-8=12

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Solution for 4(x^2-6x+9)-8=12 equation: 


Simplifying
4(x2 + -6x + 9) + -8 = 12

Reorder the terms:
4(9 + -6x + x2) + -8 = 12
(9 * 4 + -6x * 4 + x2 * 4) + -8 = 12
(36 + -24x + 4x2) + -8 = 12

Reorder the terms:
36 + -8 + -24x + 4x2 = 12

Combine like terms: 36 + -8 = 28
28 + -24x + 4x2 = 12

Solving
28 + -24x + 4x2 = 12

Solving for variable 'x'.

Reorder the terms:
28 + -12 + -24x + 4x2 = 12 + -12

Combine like terms: 28 + -12 = 16
16 + -24x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
16 + -24x + 4x2 = 0

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

Ignore the factor 4.

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

Simplifying
4 + -6x + x2 = 0

Solving
4 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6x + x2 = 0 + -4
-6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6x + x2 = -4

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -4 + 9

Reorder the terms:
9 + -6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6x + x2 = 5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -3) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -3 = 2.236067978

Simplifying
x + -3 = 2.236067978

Reorder the terms:
-3 + x = 2.236067978

Solving
-3 + x = 2.236067978

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.236067978 + 3
x = 2.236067978 + 3

Combine like terms: 2.236067978 + 3 = 5.236067978
x = 5.236067978

Simplifying
x = 5.236067978


Subproblem 2
x + -3 = -2.236067978

Simplifying
x + -3 = -2.236067978

Reorder the terms:
-3 + x = -2.236067978

Solving
-3 + x = -2.236067978

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.236067978 + 3
x = -2.236067978 + 3

Combine like terms: -2.236067978 + 3 = 0.763932022
x = 0.763932022

Simplifying
x = 0.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.236067978, 0.763932022}
Solution
x = {5.236067978, 0.763932022}

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