x(3x+24)=180

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Solution for x(3x+24)=180 equation: 


Simplifying
x(3x + 24) = 180

Reorder the terms:
x(24 + 3x) = 180
(24 * x + 3x * x) = 180
(24x + 3x2) = 180

Solving
24x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 24x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + 8x + x2 = 0

Solving
-60 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 8x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 8x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 8x + x2 = 0 + 60
8x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
8x + x2 = 60

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 60 + 16

Reorder the terms:
16 + 8x + x2 = 60 + 16

Combine like terms: 60 + 16 = 76
16 + 8x + x2 = 76

Factor a perfect square on the left side:
(x + 4)(x + 4) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + 4) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + 4 = 8.717797887

Simplifying
x + 4 = 8.717797887

Reorder the terms:
4 + x = 8.717797887

Solving
4 + x = 8.717797887

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + x = 8.717797887 + -4
x = 8.717797887 + -4

Combine like terms: 8.717797887 + -4 = 4.717797887
x = 4.717797887

Simplifying
x = 4.717797887


Subproblem 2
x + 4 = -8.717797887

Simplifying
x + 4 = -8.717797887

Reorder the terms:
4 + x = -8.717797887

Solving
4 + x = -8.717797887

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + x = -8.717797887 + -4
x = -8.717797887 + -4

Combine like terms: -8.717797887 + -4 = -12.717797887
x = -12.717797887

Simplifying
x = -12.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.717797887, -12.717797887}
Solution
x = {4.717797887, -12.717797887}

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