2x^2+2x-13=17-5x

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Solution for 2x^2+2x-13=17-5x equation: 


Simplifying
2x2 + 2x + -13 = 17 + -5x

Reorder the terms:
-13 + 2x + 2x2 = 17 + -5x

Solving
-13 + 2x + 2x2 = 17 + -5x

Solving for variable 'x'.

Reorder the terms:
-13 + -17 + 2x + 5x + 2x2 = 17 + -5x + -17 + 5x

Combine like terms: -13 + -17 = -30
-30 + 2x + 5x + 2x2 = 17 + -5x + -17 + 5x

Combine like terms: 2x + 5x = 7x
-30 + 7x + 2x2 = 17 + -5x + -17 + 5x

Reorder the terms:
-30 + 7x + 2x2 = 17 + -17 + -5x + 5x

Combine like terms: 17 + -17 = 0
-30 + 7x + 2x2 = 0 + -5x + 5x
-30 + 7x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-30 + 7x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 2.5}

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