4x^2-31x+31=-6x+6

Solution for 4x^2-31x+31=-6x+6 equation:

Simplifying
4x2 + -31x + 31 = -6x + 6

Reorder the terms:
31 + -31x + 4x2 = -6x + 6

Reorder the terms:
31 + -31x + 4x2 = 6 + -6x

Solving
31 + -31x + 4x2 = 6 + -6x

Solving for variable 'x'.

Reorder the terms:
31 + -6 + -31x + 6x + 4x2 = 6 + -6x + -6 + 6x

Combine like terms: 31 + -6 = 25
25 + -31x + 6x + 4x2 = 6 + -6x + -6 + 6x

Combine like terms: -31x + 6x = -25x
25 + -25x + 4x2 = 6 + -6x + -6 + 6x

Reorder the terms:
25 + -25x + 4x2 = 6 + -6 + -6x + 6x

Combine like terms: 6 + -6 = 0
25 + -25x + 4x2 = 0 + -6x + 6x
25 + -25x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
25 + -25x + 4x2 = 0

Factor a trinomial.
(5 + -4x)(5 + -1x) = 0

Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.25, 5}