x^2-3x-8=-2x^2+4x-2

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Solution for x^2-3x-8=-2x^2+4x-2 equation: 


Simplifying
x2 + -3x + -8 = -2x2 + 4x + -2

Reorder the terms:
-8 + -3x + x2 = -2x2 + 4x + -2

Reorder the terms:
-8 + -3x + x2 = -2 + 4x + -2x2

Solving
-8 + -3x + x2 = -2 + 4x + -2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 2 + -3x + -4x + x2 + 2x2 = -2 + 4x + -2x2 + 2 + -4x + 2x2

Combine like terms: -8 + 2 = -6
-6 + -3x + -4x + x2 + 2x2 = -2 + 4x + -2x2 + 2 + -4x + 2x2

Combine like terms: -3x + -4x = -7x
-6 + -7x + x2 + 2x2 = -2 + 4x + -2x2 + 2 + -4x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-6 + -7x + 3x2 = -2 + 4x + -2x2 + 2 + -4x + 2x2

Reorder the terms:
-6 + -7x + 3x2 = -2 + 2 + 4x + -4x + -2x2 + 2x2

Combine like terms: -2 + 2 = 0
-6 + -7x + 3x2 = 0 + 4x + -4x + -2x2 + 2x2
-6 + -7x + 3x2 = 4x + -4x + -2x2 + 2x2

Combine like terms: 4x + -4x = 0
-6 + -7x + 3x2 = 0 + -2x2 + 2x2
-6 + -7x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-6 + -7x + 3x2 = 0

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


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, 3}

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