(4x^2+12x-9)-16=9

Solution for (4x^2+12x-9)-16=9 equation:

Simplifying
(4x2 + 12x + -9) + -16 = 9

Reorder the terms:
(-9 + 12x + 4x2) + -16 = 9

Remove parenthesis around (-9 + 12x + 4x2)
-9 + 12x + 4x2 + -16 = 9

Reorder the terms:
-9 + -16 + 12x + 4x2 = 9

Combine like terms: -9 + -16 = -25
-25 + 12x + 4x2 = 9

Solving
-25 + 12x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
-25 + -9 + 12x + 4x2 = 9 + -9

Combine like terms: -25 + -9 = -34
-34 + 12x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-34 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 6x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-17 + 6x + 2x2 = 0

Solving
-17 + 6x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + 3x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 3x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 3x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 3x + x2 = 0 + 8.5
3x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
3x + x2 = 8.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 8.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8.5 + 2.25

Combine like terms: 8.5 + 2.25 = 10.75
2.25 + 3x + x2 = 10.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.75

Calculate the square root of the right side: 3.278719262

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.278719262 and -3.278719262.

Subproblem 1
x + 1.5 = 3.278719262

Simplifying
x + 1.5 = 3.278719262

Reorder the terms:
1.5 + x = 3.278719262

Solving
1.5 + x = 3.278719262

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.278719262 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.278719262 + -1.5
x = 3.278719262 + -1.5

Combine like terms: 3.278719262 + -1.5 = 1.778719262
x = 1.778719262

Simplifying
x = 1.778719262

Subproblem 2
x + 1.5 = -3.278719262

Simplifying
x + 1.5 = -3.278719262

Reorder the terms:
1.5 + x = -3.278719262

Solving
1.5 + x = -3.278719262

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.278719262 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.278719262 + -1.5
x = -3.278719262 + -1.5

Combine like terms: -3.278719262 + -1.5 = -4.778719262
x = -4.778719262

Simplifying
x = -4.778719262

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.778719262, -4.778719262}
Solution
x = {1.778719262, -4.778719262}