6x^2-21x-36=0

Solution for 6x^2-21x-36=0 equation:

Simplifying
6x2 + -21x + -36 = 0

Reorder the terms:
-36 + -21x + 6x2 = 0

Solving
-36 + -21x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -7x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-12 + -7x + 2x2 = 0

Solving
-12 + -7x + 2x2 = 0

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

Divide each side by '2'.
-6 + -3.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -3.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3.5x + x2 = 0 + 6
-3.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3.5x + x2 = 6

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 6 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 6 + 3.0625

Combine like terms: 6 + 3.0625 = 9.0625
3.0625 + -3.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.010398645 and -3.010398645.

Subproblem 1
x + -1.75 = 3.010398645

Simplifying
x + -1.75 = 3.010398645

Reorder the terms:
-1.75 + x = 3.010398645

Solving
-1.75 + x = 3.010398645

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 3.010398645 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 3.010398645 + 1.75
x = 3.010398645 + 1.75

Combine like terms: 3.010398645 + 1.75 = 4.760398645
x = 4.760398645

Simplifying
x = 4.760398645

Subproblem 2
x + -1.75 = -3.010398645

Simplifying
x + -1.75 = -3.010398645

Reorder the terms:
-1.75 + x = -3.010398645

Solving
-1.75 + x = -3.010398645

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -3.010398645 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -3.010398645 + 1.75
x = -3.010398645 + 1.75

Combine like terms: -3.010398645 + 1.75 = -1.260398645
x = -1.260398645

Simplifying
x = -1.260398645

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.760398645, -1.260398645}
Solution
x = {4.760398645, -1.260398645}