-36x^2+168x=120

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Solution for -36x^2+168x=120 equation: 


Simplifying
-36x2 + 168x = 120

Reorder the terms:
168x + -36x2 = 120

Solving
168x + -36x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 168x + -36x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 168x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-10 + 14x + -3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-10 + 14x + -3x2)' equal to zero and attempt to solve:

Simplifying
-10 + 14x + -3x2 = 0

Solving
-10 + 14x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
3.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -4.666666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -4.666666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + -3.333333333
-4.666666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-4.666666667x + x2 = -3.333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -3.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -3.333333333 + 5.444444448

Combine like terms: -3.333333333 + 5.444444448 = 2.111111115
5.444444448 + -4.666666667x + x2 = 2.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 2.111111115

Calculate the square root of the right side: 1.452966316

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 1.452966316 and -1.452966316.


Subproblem 1
x + -2.333333334 = 1.452966316

Simplifying
x + -2.333333334 = 1.452966316

Reorder the terms:
-2.333333334 + x = 1.452966316

Solving
-2.333333334 + x = 1.452966316

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 1.452966316 + 2.333333334
x = 1.452966316 + 2.333333334

Combine like terms: 1.452966316 + 2.333333334 = 3.78629965
x = 3.78629965

Simplifying
x = 3.78629965


Subproblem 2
x + -2.333333334 = -1.452966316

Simplifying
x + -2.333333334 = -1.452966316

Reorder the terms:
-2.333333334 + x = -1.452966316

Solving
-2.333333334 + x = -1.452966316

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -1.452966316 + 2.333333334
x = -1.452966316 + 2.333333334

Combine like terms: -1.452966316 + 2.333333334 = 0.880367018
x = 0.880367018

Simplifying
x = 0.880367018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.78629965, 0.880367018}
Solution
x = {3.78629965, 0.880367018}

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