(4x+16)(3x-9)=12x-36x

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Solution for (4x+16)(3x-9)=12x-36x equation: 


Simplifying
(4x + 16)(3x + -9) = 12x + -36x

Reorder the terms:
(16 + 4x)(3x + -9) = 12x + -36x

Reorder the terms:
(16 + 4x)(-9 + 3x) = 12x + -36x

Multiply (16 + 4x) * (-9 + 3x)
(16(-9 + 3x) + 4x * (-9 + 3x)) = 12x + -36x
((-9 * 16 + 3x * 16) + 4x * (-9 + 3x)) = 12x + -36x
((-144 + 48x) + 4x * (-9 + 3x)) = 12x + -36x
(-144 + 48x + (-9 * 4x + 3x * 4x)) = 12x + -36x
(-144 + 48x + (-36x + 12x2)) = 12x + -36x

Combine like terms: 48x + -36x = 12x
(-144 + 12x + 12x2) = 12x + -36x

Combine like terms: 12x + -36x = -24x
-144 + 12x + 12x2 = -24x

Solving
-144 + 12x + 12x2 = -24x

Solving for variable 'x'.

Reorder the terms:
-144 + 12x + 24x + 12x2 = -24x + 24x

Combine like terms: 12x + 24x = 36x
-144 + 36x + 12x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-144 + 36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-12 + 3x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-12 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 3x + x2 = 0

Solving
-12 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3x + x2 = 0 + 12
3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
3x + x2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + 3x + x2 = 14.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 1.5 = 3.774917218

Simplifying
x + 1.5 = 3.774917218

Reorder the terms:
1.5 + x = 3.774917218

Solving
1.5 + x = 3.774917218

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 = 3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.774917218 + -1.5
x = 3.774917218 + -1.5

Combine like terms: 3.774917218 + -1.5 = 2.274917218
x = 2.274917218

Simplifying
x = 2.274917218


Subproblem 2
x + 1.5 = -3.774917218

Simplifying
x + 1.5 = -3.774917218

Reorder the terms:
1.5 + x = -3.774917218

Solving
1.5 + x = -3.774917218

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 = -3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.774917218 + -1.5
x = -3.774917218 + -1.5

Combine like terms: -3.774917218 + -1.5 = -5.274917218
x = -5.274917218

Simplifying
x = -5.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.274917218, -5.274917218}
Solution
x = {2.274917218, -5.274917218}

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