9x-5x+10=2x^2-4x

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Solution for 9x-5x+10=2x^2-4x equation: 


Simplifying
9x + -5x + 10 = 2x2 + -4x

Reorder the terms:
10 + 9x + -5x = 2x2 + -4x

Combine like terms: 9x + -5x = 4x
10 + 4x = 2x2 + -4x

Reorder the terms:
10 + 4x = -4x + 2x2

Solving
10 + 4x = -4x + 2x2

Solving for variable 'x'.

Combine like terms: 4x + 4x = 8x
10 + 8x + -2x2 = -4x + 2x2 + 4x + -2x2

Reorder the terms:
10 + 8x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
10 + 8x + -2x2 = 0 + 2x2 + -2x2
10 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {5, -1}

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