6x^2+40x-180=0

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Solution for 6x^2+40x-180=0 equation: 


Simplifying
6x2 + 40x + -180 = 0

Reorder the terms:
-180 + 40x + 6x2 = 0

Solving
-180 + 40x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 20x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-90 + 20x + 3x2 = 0

Solving
-90 + 20x + 3x2 = 0

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

Divide each side by '3'.
-30 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 6.666666667x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 6.666666667x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 6.666666667x + x2 = 0 + 30
6.666666667x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
6.666666667x + x2 = 30

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 30 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 30 + 11.11111112

Combine like terms: 30 + 11.11111112 = 41.11111112
11.11111112 + 6.666666667x + x2 = 41.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 41.11111112

Calculate the square root of the right side: 6.411794688

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 6.411794688 and -6.411794688.


Subproblem 1
x + 3.333333334 = 6.411794688

Simplifying
x + 3.333333334 = 6.411794688

Reorder the terms:
3.333333334 + x = 6.411794688

Solving
3.333333334 + x = 6.411794688

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 6.411794688 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 6.411794688 + -3.333333334
x = 6.411794688 + -3.333333334

Combine like terms: 6.411794688 + -3.333333334 = 3.078461354
x = 3.078461354

Simplifying
x = 3.078461354


Subproblem 2
x + 3.333333334 = -6.411794688

Simplifying
x + 3.333333334 = -6.411794688

Reorder the terms:
3.333333334 + x = -6.411794688

Solving
3.333333334 + x = -6.411794688

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -6.411794688 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -6.411794688 + -3.333333334
x = -6.411794688 + -3.333333334

Combine like terms: -6.411794688 + -3.333333334 = -9.745128022
x = -9.745128022

Simplifying
x = -9.745128022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.078461354, -9.745128022}
Solution
x = {3.078461354, -9.745128022}

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