3X^2-5X-12=0

Solution for 3X^2-5X-12=0 equation:

Simplifying
3X2 + -5X + -12 = 0

Reorder the terms:
-12 + -5X + 3X2 = 0

Solving
-12 + -5X + 3X2 = 0

Solving for variable 'X'.

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

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 '(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
Solution
X = {-1.333333333, 3}