2x^2+2x-10=x^2-11x+20

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Solution for 2x^2+2x-10=x^2-11x+20 equation: 


Simplifying
2x2 + 2x + -10 = x2 + -11x + 20

Reorder the terms:
-10 + 2x + 2x2 = x2 + -11x + 20

Reorder the terms:
-10 + 2x + 2x2 = 20 + -11x + x2

Solving
-10 + 2x + 2x2 = 20 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + -20 + 2x + 11x + 2x2 + -1x2 = 20 + -11x + x2 + -20 + 11x + -1x2

Combine like terms: -10 + -20 = -30
-30 + 2x + 11x + 2x2 + -1x2 = 20 + -11x + x2 + -20 + 11x + -1x2

Combine like terms: 2x + 11x = 13x
-30 + 13x + 2x2 + -1x2 = 20 + -11x + x2 + -20 + 11x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-30 + 13x + 1x2 = 20 + -11x + x2 + -20 + 11x + -1x2

Reorder the terms:
-30 + 13x + 1x2 = 20 + -20 + -11x + 11x + x2 + -1x2

Combine like terms: 20 + -20 = 0
-30 + 13x + 1x2 = 0 + -11x + 11x + x2 + -1x2
-30 + 13x + 1x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
-30 + 13x + 1x2 = 0 + x2 + -1x2
-30 + 13x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + 13x + 1x2 = 0

Factor a trinomial.
(-15 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15, 2}

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