x^2-2x-10=-2x^2+x+8

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Solution for x^2-2x-10=-2x^2+x+8 equation:


Simplifying
x2 + -2x + -10 = -2x2 + x + 8

Reorder the terms:
-10 + -2x + x2 = -2x2 + x + 8

Reorder the terms:
-10 + -2x + x2 = 8 + x + -2x2

Solving
-10 + -2x + x2 = 8 + x + -2x2

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + -2x + -1x + x2 + 2x2 = 8 + x + -2x2 + -8 + -1x + 2x2

Combine like terms: -10 + -8 = -18
-18 + -2x + -1x + x2 + 2x2 = 8 + x + -2x2 + -8 + -1x + 2x2

Combine like terms: -2x + -1x = -3x
-18 + -3x + x2 + 2x2 = 8 + x + -2x2 + -8 + -1x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-18 + -3x + 3x2 = 8 + x + -2x2 + -8 + -1x + 2x2

Reorder the terms:
-18 + -3x + 3x2 = 8 + -8 + x + -1x + -2x2 + 2x2

Combine like terms: 8 + -8 = 0
-18 + -3x + 3x2 = 0 + x + -1x + -2x2 + 2x2
-18 + -3x + 3x2 = x + -1x + -2x2 + 2x2

Combine like terms: x + -1x = 0
-18 + -3x + 3x2 = 0 + -2x2 + 2x2
-18 + -3x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-18 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-2, 3}

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