12x^2+18x-16=0

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Solution for 12x^2+18x-16=0 equation: 


Simplifying
12x2 + 18x + -16 = 0

Reorder the terms:
-16 + 18x + 12x2 = 0

Solving
-16 + 18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 9x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 9x + 6x2)' equal to zero and attempt to solve:

Simplifying
-8 + 9x + 6x2 = 0

Solving
-8 + 9x + 6x2 = 0

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

Divide each side by '6'.
-1.333333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.5x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.5x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + 1.333333333
1.5x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.5x + x2 = 1.333333333

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 = 1.333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 1.333333333 + 0.5625

Combine like terms: 1.333333333 + 0.5625 = 1.895833333
0.5625 + 1.5x + x2 = 1.895833333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 1.895833333

Calculate the square root of the right side: 1.376892637

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.376892637 and -1.376892637.


Subproblem 1
x + 0.75 = 1.376892637

Simplifying
x + 0.75 = 1.376892637

Reorder the terms:
0.75 + x = 1.376892637

Solving
0.75 + x = 1.376892637

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 = 1.376892637 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.376892637 + -0.75
x = 1.376892637 + -0.75

Combine like terms: 1.376892637 + -0.75 = 0.626892637
x = 0.626892637

Simplifying
x = 0.626892637


Subproblem 2
x + 0.75 = -1.376892637

Simplifying
x + 0.75 = -1.376892637

Reorder the terms:
0.75 + x = -1.376892637

Solving
0.75 + x = -1.376892637

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 = -1.376892637 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.376892637 + -0.75
x = -1.376892637 + -0.75

Combine like terms: -1.376892637 + -0.75 = -2.126892637
x = -2.126892637

Simplifying
x = -2.126892637


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.626892637, -2.126892637}
Solution
x = {0.626892637, -2.126892637}

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