2x^2+2x-17=8-3x

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Solution for 2x^2+2x-17=8-3x equation: 


Simplifying
2x2 + 2x + -17 = 8 + -3x

Reorder the terms:
-17 + 2x + 2x2 = 8 + -3x

Solving
-17 + 2x + 2x2 = 8 + -3x

Solving for variable 'x'.

Reorder the terms:
-17 + -8 + 2x + 3x + 2x2 = 8 + -3x + -8 + 3x

Combine like terms: -17 + -8 = -25
-25 + 2x + 3x + 2x2 = 8 + -3x + -8 + 3x

Combine like terms: 2x + 3x = 5x
-25 + 5x + 2x2 = 8 + -3x + -8 + 3x

Reorder the terms:
-25 + 5x + 2x2 = 8 + -8 + -3x + 3x

Combine like terms: 8 + -8 = 0
-25 + 5x + 2x2 = 0 + -3x + 3x
-25 + 5x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-25 + 5x + 2x2 = 0

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


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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-5, 2.5}

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