x^2-4x-8=-2x^2+7x-4

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Solution for x^2-4x-8=-2x^2+7x-4 equation: 


Simplifying
x2 + -4x + -8 = -2x2 + 7x + -4

Reorder the terms:
-8 + -4x + x2 = -2x2 + 7x + -4

Reorder the terms:
-8 + -4x + x2 = -4 + 7x + -2x2

Solving
-8 + -4x + x2 = -4 + 7x + -2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 4 + -4x + -7x + x2 + 2x2 = -4 + 7x + -2x2 + 4 + -7x + 2x2

Combine like terms: -8 + 4 = -4
-4 + -4x + -7x + x2 + 2x2 = -4 + 7x + -2x2 + 4 + -7x + 2x2

Combine like terms: -4x + -7x = -11x
-4 + -11x + x2 + 2x2 = -4 + 7x + -2x2 + 4 + -7x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-4 + -11x + 3x2 = -4 + 7x + -2x2 + 4 + -7x + 2x2

Reorder the terms:
-4 + -11x + 3x2 = -4 + 4 + 7x + -7x + -2x2 + 2x2

Combine like terms: -4 + 4 = 0
-4 + -11x + 3x2 = 0 + 7x + -7x + -2x2 + 2x2
-4 + -11x + 3x2 = 7x + -7x + -2x2 + 2x2

Combine like terms: 7x + -7x = 0
-4 + -11x + 3x2 = 0 + -2x2 + 2x2
-4 + -11x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-4 + -11x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(4 + -1x) = 0


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
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
Solution
x = {-0.3333333333, 4}

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