3x^2+5x-138=0

Solution for 3x^2+5x-138=0 equation:

Simplifying
3x2 + 5x + -138 = 0

Reorder the terms:
-138 + 5x + 3x2 = 0

Solving
-138 + 5x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-23 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-23 + -3x)' equal to zero and attempt to solve:

Simplifying
-23 + -3x = 0

Solving
-23 + -3x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -3x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -3x = 0 + 23
-3x = 0 + 23

Combine like terms: 0 + 23 = 23
-3x = 23

Divide each side by '-3'.
x = -7.666666667

Simplifying
x = -7.666666667
Subproblem 2
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
Solution
x = {-7.666666667, 6}