4x^2-27x+31=-2x+6

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Solution for 4x^2-27x+31=-2x+6 equation: 


Simplifying
4x2 + -27x + 31 = -2x + 6

Reorder the terms:
31 + -27x + 4x2 = -2x + 6

Reorder the terms:
31 + -27x + 4x2 = 6 + -2x

Solving
31 + -27x + 4x2 = 6 + -2x

Solving for variable 'x'.

Reorder the terms:
31 + -6 + -27x + 2x + 4x2 = 6 + -2x + -6 + 2x

Combine like terms: 31 + -6 = 25
25 + -27x + 2x + 4x2 = 6 + -2x + -6 + 2x

Combine like terms: -27x + 2x = -25x
25 + -25x + 4x2 = 6 + -2x + -6 + 2x

Reorder the terms:
25 + -25x + 4x2 = 6 + -6 + -2x + 2x

Combine like terms: 6 + -6 = 0
25 + -25x + 4x2 = 0 + -2x + 2x
25 + -25x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 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}

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