0=5x^2-31x+6

Solution for 0=5x^2-31x+6 equation:

Simplifying
0 = 5x2 + -31x + 6

Reorder the terms:
0 = 6 + -31x + 5x2

Solving
0 = 6 + -31x + 5x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6
Subproblem 2
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
Solution
x = {6, 0.2}