x^2+2x=4x+4+31

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


Simplifying
x2 + 2x = 4x + 4 + 31

Reorder the terms:
2x + x2 = 4x + 4 + 31

Reorder the terms:
2x + x2 = 4 + 31 + 4x

Combine like terms: 4 + 31 = 35
2x + x2 = 35 + 4x

Solving
2x + x2 = 35 + 4x

Solving for variable 'x'.

Reorder the terms:
-35 + 2x + -4x + x2 = 35 + 4x + -35 + -4x

Combine like terms: 2x + -4x = -2x
-35 + -2x + x2 = 35 + 4x + -35 + -4x

Reorder the terms:
-35 + -2x + x2 = 35 + -35 + 4x + -4x

Combine like terms: 35 + -35 = 0
-35 + -2x + x2 = 0 + 4x + -4x
-35 + -2x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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