2x^2-3x-8=x^2+20

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Solution for 2x^2-3x-8=x^2+20 equation: 


Simplifying
2x2 + -3x + -8 = x2 + 20

Reorder the terms:
-8 + -3x + 2x2 = x2 + 20

Reorder the terms:
-8 + -3x + 2x2 = 20 + x2

Solving
-8 + -3x + 2x2 = 20 + x2

Solving for variable 'x'.

Reorder the terms:
-8 + -20 + -3x + 2x2 + -1x2 = 20 + x2 + -20 + -1x2

Combine like terms: -8 + -20 = -28
-28 + -3x + 2x2 + -1x2 = 20 + x2 + -20 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-28 + -3x + 1x2 = 20 + x2 + -20 + -1x2

Reorder the terms:
-28 + -3x + 1x2 = 20 + -20 + x2 + -1x2

Combine like terms: 20 + -20 = 0
-28 + -3x + 1x2 = 0 + x2 + -1x2
-28 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + -3x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -1x) = 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 '(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 = {-4, 7}

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