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.
(-6 + -1x)(67 + -6x) = 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 '(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
Solution
x = {-6, 11.16666667}