6x^2+33x-24=0

Solution for 6x^2+33x-24=0 equation:

Simplifying
6x2 + 33x + -24 = 0

Reorder the terms:
-24 + 33x + 6x2 = 0

Solving
-24 + 33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 11x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-8 + 11x + 2x2 = 0

Solving
-8 + 11x + 2x2 = 0

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

Divide each side by '2'.
-4 + 5.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5.5x + x2 = 0 + 4
5.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
5.5x + x2 = 4

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 4 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 4 + 7.5625

Combine like terms: 4 + 7.5625 = 11.5625
7.5625 + 5.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + 2.75) equal to 3.400367627 and -3.400367627.

Subproblem 1
x + 2.75 = 3.400367627

Simplifying
x + 2.75 = 3.400367627

Reorder the terms:
2.75 + x = 3.400367627

Solving
2.75 + x = 3.400367627

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 3.400367627 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 3.400367627 + -2.75
x = 3.400367627 + -2.75

Combine like terms: 3.400367627 + -2.75 = 0.650367627
x = 0.650367627

Simplifying
x = 0.650367627

Subproblem 2
x + 2.75 = -3.400367627

Simplifying
x + 2.75 = -3.400367627

Reorder the terms:
2.75 + x = -3.400367627

Solving
2.75 + x = -3.400367627

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -3.400367627 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -3.400367627 + -2.75
x = -3.400367627 + -2.75

Combine like terms: -3.400367627 + -2.75 = -6.150367627
x = -6.150367627

Simplifying
x = -6.150367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.650367627, -6.150367627}
Solution
x = {0.650367627, -6.150367627}