6x^2+9x+-8-12=

Solution for 6x^2+9x+-8-12= equation:

Simplifying
6x2 + 9x + -8 + -12 = 0

Reorder the terms:
-8 + -12 + 9x + 6x2 = 0

Combine like terms: -8 + -12 = -20
-20 + 9x + 6x2 = 0

Solving
-20 + 9x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-3.333333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 1.5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 1.5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + 3.333333333
1.5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
1.5x + x2 = 3.333333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 3.333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 3.333333333 + 0.5625

Combine like terms: 3.333333333 + 0.5625 = 3.895833333
0.5625 + 1.5x + x2 = 3.895833333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 3.895833333

Calculate the square root of the right side: 1.973786547

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.973786547 and -1.973786547.

Subproblem 1
x + 0.75 = 1.973786547

Simplifying
x + 0.75 = 1.973786547

Reorder the terms:
0.75 + x = 1.973786547

Solving
0.75 + x = 1.973786547

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.973786547 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.973786547 + -0.75
x = 1.973786547 + -0.75

Combine like terms: 1.973786547 + -0.75 = 1.223786547
x = 1.223786547

Simplifying
x = 1.223786547

Subproblem 2
x + 0.75 = -1.973786547

Simplifying
x + 0.75 = -1.973786547

Reorder the terms:
0.75 + x = -1.973786547

Solving
0.75 + x = -1.973786547

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.973786547 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.973786547 + -0.75
x = -1.973786547 + -0.75

Combine like terms: -1.973786547 + -0.75 = -2.723786547
x = -2.723786547

Simplifying
x = -2.723786547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.223786547, -2.723786547}