3x^2+30x-336=0

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Solution for 3x^2+30x-336=0 equation: 


Simplifying
3x2 + 30x + -336 = 0

Reorder the terms:
-336 + 30x + 3x2 = 0

Solving
-336 + 30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-112 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-112 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-112 + 10x + x2 = 0

Solving
-112 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + 10x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + 10x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + 10x + x2 = 0 + 112
10x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
10x + x2 = 112

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 112 + 25

Reorder the terms:
25 + 10x + x2 = 112 + 25

Combine like terms: 112 + 25 = 137
25 + 10x + x2 = 137

Factor a perfect square on the left side:
(x + 5)(x + 5) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(x + 5) equal to 11.704699911 and -11.704699911.


Subproblem 1
x + 5 = 11.704699911

Simplifying
x + 5 = 11.704699911

Reorder the terms:
5 + x = 11.704699911

Solving
5 + x = 11.704699911

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 11.704699911 + -5

Combine like terms: 5 + -5 = 0
0 + x = 11.704699911 + -5
x = 11.704699911 + -5

Combine like terms: 11.704699911 + -5 = 6.704699911
x = 6.704699911

Simplifying
x = 6.704699911


Subproblem 2
x + 5 = -11.704699911

Simplifying
x + 5 = -11.704699911

Reorder the terms:
5 + x = -11.704699911

Solving
5 + x = -11.704699911

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -11.704699911 + -5

Combine like terms: 5 + -5 = 0
0 + x = -11.704699911 + -5
x = -11.704699911 + -5

Combine like terms: -11.704699911 + -5 = -16.704699911
x = -16.704699911

Simplifying
x = -16.704699911


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.704699911, -16.704699911}
Solution
x = {6.704699911, -16.704699911}

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