5x+20-3x=2x^2+8x

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Solution for 5x+20-3x=2x^2+8x equation: 


Simplifying
5x + 20 + -3x = 2x2 + 8x

Reorder the terms:
20 + 5x + -3x = 2x2 + 8x

Combine like terms: 5x + -3x = 2x
20 + 2x = 2x2 + 8x

Reorder the terms:
20 + 2x = 8x + 2x2

Solving
20 + 2x = 8x + 2x2

Solving for variable 'x'.

Combine like terms: 2x + -8x = -6x
20 + -6x + -2x2 = 8x + 2x2 + -8x + -2x2

Reorder the terms:
20 + -6x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
20 + -6x + -2x2 = 0 + 2x2 + -2x2
20 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -3x + -1x2) = 0

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

Ignore the factor 2.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {2, -5}

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