24x^2+336x-135=0

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Solution for 24x^2+336x-135=0 equation: 


Simplifying
24x2 + 336x + -135 = 0

Reorder the terms:
-135 + 336x + 24x2 = 0

Solving
-135 + 336x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + 112x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-45 + 112x + 8x2)' equal to zero and attempt to solve:

Simplifying
-45 + 112x + 8x2 = 0

Solving
-45 + 112x + 8x2 = 0

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

Divide each side by '8'.
-5.625 + 14x + x2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + 14x + 5.625 + x2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + 14x + x2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + 14x + x2 = 0 + 5.625
14x + x2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
14x + x2 = 5.625

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 = 5.625 + 49

Reorder the terms:
49 + 14x + x2 = 5.625 + 49

Combine like terms: 5.625 + 49 = 54.625
49 + 14x + x2 = 54.625

Factor a perfect square on the left side:
(x + 7)(x + 7) = 54.625

Calculate the square root of the right side: 7.39087275

Break this problem into two subproblems by setting 
(x + 7) equal to 7.39087275 and -7.39087275.


Subproblem 1
x + 7 = 7.39087275

Simplifying
x + 7 = 7.39087275

Reorder the terms:
7 + x = 7.39087275

Solving
7 + x = 7.39087275

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 = 7.39087275 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.39087275 + -7
x = 7.39087275 + -7

Combine like terms: 7.39087275 + -7 = 0.39087275
x = 0.39087275

Simplifying
x = 0.39087275


Subproblem 2
x + 7 = -7.39087275

Simplifying
x + 7 = -7.39087275

Reorder the terms:
7 + x = -7.39087275

Solving
7 + x = -7.39087275

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 = -7.39087275 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.39087275 + -7
x = -7.39087275 + -7

Combine like terms: -7.39087275 + -7 = -14.39087275
x = -14.39087275

Simplifying
x = -14.39087275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.39087275, -14.39087275}
Solution
x = {0.39087275, -14.39087275}

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