-2x^2-x=-9x+8

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Solution for -2x^2-x=-9x+8 equation: 


Simplifying
-2x2 + -1x = -9x + 8

Reorder the terms:
-1x + -2x2 = -9x + 8

Reorder the terms:
-1x + -2x2 = 8 + -9x

Solving
-1x + -2x2 = 8 + -9x

Solving for variable 'x'.

Reorder the terms:
-8 + -1x + 9x + -2x2 = 8 + -9x + -8 + 9x

Combine like terms: -1x + 9x = 8x
-8 + 8x + -2x2 = 8 + -9x + -8 + 9x

Reorder the terms:
-8 + 8x + -2x2 = 8 + -8 + -9x + 9x

Combine like terms: 8 + -8 = 0
-8 + 8x + -2x2 = 0 + -9x + 9x
-8 + 8x + -2x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-8 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 4x + -1x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2

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 = {2, 2}

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