6x(2x+36)=180

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Solution for 6x(2x+36)=180 equation: 


Simplifying
6x(2x + 36) = 180

Reorder the terms:
6x(36 + 2x) = 180
(36 * 6x + 2x * 6x) = 180
(216x + 12x2) = 180

Solving
216x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 216x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 216x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-15 + 18x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-15 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 18x + x2 = 0

Solving
-15 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 18x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 18x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 18x + x2 = 0 + 15
18x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
18x + x2 = 15

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 15 + 81

Reorder the terms:
81 + 18x + x2 = 15 + 81

Combine like terms: 15 + 81 = 96
81 + 18x + x2 = 96

Factor a perfect square on the left side:
(x + 9)(x + 9) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + 9) equal to 9.797958971 and -9.797958971.


Subproblem 1
x + 9 = 9.797958971

Simplifying
x + 9 = 9.797958971

Reorder the terms:
9 + x = 9.797958971

Solving
9 + x = 9.797958971

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 9.797958971 + -9

Combine like terms: 9 + -9 = 0
0 + x = 9.797958971 + -9
x = 9.797958971 + -9

Combine like terms: 9.797958971 + -9 = 0.797958971
x = 0.797958971

Simplifying
x = 0.797958971


Subproblem 2
x + 9 = -9.797958971

Simplifying
x + 9 = -9.797958971

Reorder the terms:
9 + x = -9.797958971

Solving
9 + x = -9.797958971

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -9.797958971 + -9

Combine like terms: 9 + -9 = 0
0 + x = -9.797958971 + -9
x = -9.797958971 + -9

Combine like terms: -9.797958971 + -9 = -18.797958971
x = -18.797958971

Simplifying
x = -18.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.797958971, -18.797958971}
Solution
x = {0.797958971, -18.797958971}

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