4x(96+3x)=180

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Solution for 4x(96+3x)=180 equation: 


Simplifying
4x(96 + 3x) = 180
(96 * 4x + 3x * 4x) = 180
(384x + 12x2) = 180

Solving
384x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 384x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 384x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-15 + 32x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-15 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 32x + x2 = 0

Solving
-15 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 32x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 32x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 32x + x2 = 0 + 15
32x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
32x + x2 = 15

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = 15 + 256

Reorder the terms:
256 + 32x + x2 = 15 + 256

Combine like terms: 15 + 256 = 271
256 + 32x + x2 = 271

Factor a perfect square on the left side:
(x + 16)(x + 16) = 271

Calculate the square root of the right side: 16.462077633

Break this problem into two subproblems by setting 
(x + 16) equal to 16.462077633 and -16.462077633.


Subproblem 1
x + 16 = 16.462077633

Simplifying
x + 16 = 16.462077633

Reorder the terms:
16 + x = 16.462077633

Solving
16 + x = 16.462077633

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 16.462077633 + -16

Combine like terms: 16 + -16 = 0
0 + x = 16.462077633 + -16
x = 16.462077633 + -16

Combine like terms: 16.462077633 + -16 = 0.462077633
x = 0.462077633

Simplifying
x = 0.462077633


Subproblem 2
x + 16 = -16.462077633

Simplifying
x + 16 = -16.462077633

Reorder the terms:
16 + x = -16.462077633

Solving
16 + x = -16.462077633

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -16.462077633 + -16

Combine like terms: 16 + -16 = 0
0 + x = -16.462077633 + -16
x = -16.462077633 + -16

Combine like terms: -16.462077633 + -16 = -32.462077633
x = -32.462077633

Simplifying
x = -32.462077633


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.462077633, -32.462077633}
Solution
x = {0.462077633, -32.462077633}

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