=3x^2-5x-12

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Solution for =3x^2-5x-12 equation: 


Simplifying
0 = 3x2 + -5x + -12

Reorder the terms:
0 = -12 + -5x + 3x2

Solving
0 = -12 + -5x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + 5x + -3x2 = -12 + -5x + 3x2 + 12 + 5x + -3x2

Reorder the terms:
12 + 5x + -3x2 = -12 + 12 + -5x + 5x + 3x2 + -3x2

Combine like terms: -12 + 12 = 0
12 + 5x + -3x2 = 0 + -5x + 5x + 3x2 + -3x2
12 + 5x + -3x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
12 + 5x + -3x2 = 0 + 3x2 + -3x2
12 + 5x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + 5x + -3x2 = 0

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, -1.333333333}

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