3x^2-2x-120=0

Solution for 3x^2-2x-120=0 equation:

Simplifying
3x2 + -2x + -120 = 0

Reorder the terms:
-120 + -2x + 3x2 = 0

Solving
-120 + -2x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(20 + -3x) = 0

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(20 + -3x)' equal to zero and attempt to solve:

Simplifying
20 + -3x = 0

Solving
20 + -3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3x = 0 + -20
-3x = 0 + -20

Combine like terms: 0 + -20 = -20
-3x = -20

Divide each side by '-3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {-6, 6.666666667}