0=12x^2-10x-8

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Solution for 0=12x^2-10x-8 equation: 


Simplifying
0 = 12x2 + -10x + -8

Reorder the terms:
0 = -8 + -10x + 12x2

Solving
0 = -8 + -10x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 10x + -12x2 = -8 + -10x + 12x2 + 8 + 10x + -12x2

Reorder the terms:
8 + 10x + -12x2 = -8 + 8 + -10x + 10x + 12x2 + -12x2

Combine like terms: -8 + 8 = 0
8 + 10x + -12x2 = 0 + -10x + 10x + 12x2 + -12x2
8 + 10x + -12x2 = -10x + 10x + 12x2 + -12x2

Combine like terms: -10x + 10x = 0
8 + 10x + -12x2 = 0 + 12x2 + -12x2
8 + 10x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
8 + 10x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5x + -6x2) = 0

Factor a trinomial.
2((4 + -3x)(1 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {1.333333333, -0.5}

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