5x^2+7x-17=25-22x

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Solution for 5x^2+7x-17=25-22x equation: 


Simplifying
5x2 + 7x + -17 = 25 + -22x

Reorder the terms:
-17 + 7x + 5x2 = 25 + -22x

Solving
-17 + 7x + 5x2 = 25 + -22x

Solving for variable 'x'.

Reorder the terms:
-17 + -25 + 7x + 22x + 5x2 = 25 + -22x + -25 + 22x

Combine like terms: -17 + -25 = -42
-42 + 7x + 22x + 5x2 = 25 + -22x + -25 + 22x

Combine like terms: 7x + 22x = 29x
-42 + 29x + 5x2 = 25 + -22x + -25 + 22x

Reorder the terms:
-42 + 29x + 5x2 = 25 + -25 + -22x + 22x

Combine like terms: 25 + -25 = 0
-42 + 29x + 5x2 = 0 + -22x + 22x
-42 + 29x + 5x2 = -22x + 22x

Combine like terms: -22x + 22x = 0
-42 + 29x + 5x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -5x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-7, 1.2}

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