=12x^2-3x-15

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Solution for =12x^2-3x-15 equation: 


Simplifying
0 = 12x2 + -3x + -15

Reorder the terms:
0 = -15 + -3x + 12x2

Solving
0 = -15 + -3x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 3x + -12x2 = -15 + -3x + 12x2 + 15 + 3x + -12x2

Reorder the terms:
15 + 3x + -12x2 = -15 + 15 + -3x + 3x + 12x2 + -12x2

Combine like terms: -15 + 15 = 0
15 + 3x + -12x2 = 0 + -3x + 3x + 12x2 + -12x2
15 + 3x + -12x2 = -3x + 3x + 12x2 + -12x2

Combine like terms: -3x + 3x = 0
15 + 3x + -12x2 = 0 + 12x2 + -12x2
15 + 3x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
15 + 3x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + x + -4x2) = 0

Factor a trinomial.
3((5 + -4x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {1.25, -1}

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