5x^2+10x-23=22-6x

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Solution for 5x^2+10x-23=22-6x equation: 


Simplifying
5x2 + 10x + -23 = 22 + -6x

Reorder the terms:
-23 + 10x + 5x2 = 22 + -6x

Solving
-23 + 10x + 5x2 = 22 + -6x

Solving for variable 'x'.

Reorder the terms:
-23 + -22 + 10x + 6x + 5x2 = 22 + -6x + -22 + 6x

Combine like terms: -23 + -22 = -45
-45 + 10x + 6x + 5x2 = 22 + -6x + -22 + 6x

Combine like terms: 10x + 6x = 16x
-45 + 16x + 5x2 = 22 + -6x + -22 + 6x

Reorder the terms:
-45 + 16x + 5x2 = 22 + -22 + -6x + 6x

Combine like terms: 22 + -22 = 0
-45 + 16x + 5x2 = 0 + -6x + 6x
-45 + 16x + 5x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-45 + 16x + 5x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -5x) = 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 '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {-5, 1.8}

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