x^2-13x+36=2x^2-16x+32

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Solution for x^2-13x+36=2x^2-16x+32 equation: 


Simplifying
x2 + -13x + 36 = 2x2 + -16x + 32

Reorder the terms:
36 + -13x + x2 = 2x2 + -16x + 32

Reorder the terms:
36 + -13x + x2 = 32 + -16x + 2x2

Solving
36 + -13x + x2 = 32 + -16x + 2x2

Solving for variable 'x'.

Reorder the terms:
36 + -32 + -13x + 16x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: 36 + -32 = 4
4 + -13x + 16x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: -13x + 16x = 3x
4 + 3x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: x2 + -2x2 = -1x2
4 + 3x + -1x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Reorder the terms:
4 + 3x + -1x2 = 32 + -32 + -16x + 16x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
4 + 3x + -1x2 = 0 + -16x + 16x + 2x2 + -2x2
4 + 3x + -1x2 = -16x + 16x + 2x2 + -2x2

Combine like terms: -16x + 16x = 0
4 + 3x + -1x2 = 0 + 2x2 + -2x2
4 + 3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + 3x + -1x2 = 0

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


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {4, -1}

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