x(3x+12)+90=180

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Solution for x(3x+12)+90=180 equation: 


Simplifying
x(3x + 12) + 90 = 180

Reorder the terms:
x(12 + 3x) + 90 = 180
(12 * x + 3x * x) + 90 = 180
(12x + 3x2) + 90 = 180

Reorder the terms:
90 + 12x + 3x2 = 180

Solving
90 + 12x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
90 + -180 + 12x + 3x2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + 12x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-30 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 4x + x2 = 0

Solving
-30 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 4x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4x + x2 = 0 + 30
4x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
4x + x2 = 30

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 30 + 4

Reorder the terms:
4 + 4x + x2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + 4x + x2 = 34

Factor a perfect square on the left side:
(x + 2)(x + 2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + 2) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + 2 = 5.830951895

Simplifying
x + 2 = 5.830951895

Reorder the terms:
2 + x = 5.830951895

Solving
2 + x = 5.830951895

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + x = 5.830951895 + -2
x = 5.830951895 + -2

Combine like terms: 5.830951895 + -2 = 3.830951895
x = 3.830951895

Simplifying
x = 3.830951895


Subproblem 2
x + 2 = -5.830951895

Simplifying
x + 2 = -5.830951895

Reorder the terms:
2 + x = -5.830951895

Solving
2 + x = -5.830951895

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + x = -5.830951895 + -2
x = -5.830951895 + -2

Combine like terms: -5.830951895 + -2 = -7.830951895
x = -7.830951895

Simplifying
x = -7.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.830951895, -7.830951895}
Solution
x = {3.830951895, -7.830951895}

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