(6x)(x+16)=180

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Solution for (6x)(x+16)=180 equation: 


Simplifying
(6x)(x + 16) = 180

Remove parenthesis around (6x)
6x(x + 16) = 180

Reorder the terms:
6x(16 + x) = 180
(16 * 6x + x * 6x) = 180
(96x + 6x2) = 180

Solving
96x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 96x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 96x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 16x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 16x + x2 = 0

Solving
-30 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 16x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 16x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 16x + x2 = 0 + 30
16x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
16x + x2 = 30

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 30 + 64

Reorder the terms:
64 + 16x + x2 = 30 + 64

Combine like terms: 30 + 64 = 94
64 + 16x + x2 = 94

Factor a perfect square on the left side:
(x + 8)(x + 8) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + 8) equal to 9.695359715 and -9.695359715.


Subproblem 1
x + 8 = 9.695359715

Simplifying
x + 8 = 9.695359715

Reorder the terms:
8 + x = 9.695359715

Solving
8 + x = 9.695359715

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 9.695359715 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.695359715 + -8
x = 9.695359715 + -8

Combine like terms: 9.695359715 + -8 = 1.695359715
x = 1.695359715

Simplifying
x = 1.695359715


Subproblem 2
x + 8 = -9.695359715

Simplifying
x + 8 = -9.695359715

Reorder the terms:
8 + x = -9.695359715

Solving
8 + x = -9.695359715

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -9.695359715 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.695359715 + -8
x = -9.695359715 + -8

Combine like terms: -9.695359715 + -8 = -17.695359715
x = -17.695359715

Simplifying
x = -17.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.695359715, -17.695359715}
Solution
x = {1.695359715, -17.695359715}

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