6x^2+84x-240=0

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Solution for 6x^2+84x-240=0 equation: 


Simplifying
6x2 + 84x + -240 = 0

Reorder the terms:
-240 + 84x + 6x2 = 0

Solving
-240 + 84x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-40 + 14x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-40 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + 14x + x2 = 0

Solving
-40 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 14x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 14x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 14x + x2 = 0 + 40
14x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
14x + x2 = 40

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 40 + 49

Reorder the terms:
49 + 14x + x2 = 40 + 49

Combine like terms: 40 + 49 = 89
49 + 14x + x2 = 89

Factor a perfect square on the left side:
(x + 7)(x + 7) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + 7) equal to 9.433981132 and -9.433981132.


Subproblem 1
x + 7 = 9.433981132

Simplifying
x + 7 = 9.433981132

Reorder the terms:
7 + x = 9.433981132

Solving
7 + x = 9.433981132

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 9.433981132 + -7

Combine like terms: 7 + -7 = 0
0 + x = 9.433981132 + -7
x = 9.433981132 + -7

Combine like terms: 9.433981132 + -7 = 2.433981132
x = 2.433981132

Simplifying
x = 2.433981132


Subproblem 2
x + 7 = -9.433981132

Simplifying
x + 7 = -9.433981132

Reorder the terms:
7 + x = -9.433981132

Solving
7 + x = -9.433981132

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -9.433981132 + -7

Combine like terms: 7 + -7 = 0
0 + x = -9.433981132 + -7
x = -9.433981132 + -7

Combine like terms: -9.433981132 + -7 = -16.433981132
x = -16.433981132

Simplifying
x = -16.433981132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.433981132, -16.433981132}
Solution
x = {2.433981132, -16.433981132}

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