5x^2=31x-6

Solution for 5x^2=31x-6 equation:

Simplifying
5x2 = 31x + -6

Reorder the terms:
5x2 = -6 + 31x

Solving
5x2 = -6 + 31x

Solving for variable 'x'.

Reorder the terms:
6 + -31x + 5x2 = -6 + 31x + 6 + -31x

Reorder the terms:
6 + -31x + 5x2 = -6 + 6 + 31x + -31x

Combine like terms: -6 + 6 = 0
6 + -31x + 5x2 = 0 + 31x + -31x
6 + -31x + 5x2 = 31x + -31x

Combine like terms: 31x + -31x = 0
6 + -31x + 5x2 = 0

Factor a trinomial.
(1 + -5x)(6 + -1x) = 0

Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
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 = {0.2, 6}