6x^2+31x-402=0

Solution for 6x^2+31x-402=0 equation:

Simplifying
6x2 + 31x + -402 = 0

Reorder the terms:
-402 + 31x + 6x2 = 0

Solving
-402 + 31x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-67 + -6x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-67 + -6x)' equal to zero and attempt to solve:

Simplifying
-67 + -6x = 0

Solving
-67 + -6x = 0

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

Add '67' to each side of the equation.
-67 + 67 + -6x = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -6x = 0 + 67
-6x = 0 + 67

Combine like terms: 0 + 67 = 67
-6x = 67

Divide each side by '-6'.
x = -11.16666667

Simplifying
x = -11.16666667
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 = {-11.16666667, 6}