5x^2-10x+15=24+2x

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Solution for 5x^2-10x+15=24+2x equation: 


Simplifying
5x2 + -10x + 15 = 24 + 2x

Reorder the terms:
15 + -10x + 5x2 = 24 + 2x

Solving
15 + -10x + 5x2 = 24 + 2x

Solving for variable 'x'.

Reorder the terms:
15 + -24 + -10x + -2x + 5x2 = 24 + 2x + -24 + -2x

Combine like terms: 15 + -24 = -9
-9 + -10x + -2x + 5x2 = 24 + 2x + -24 + -2x

Combine like terms: -10x + -2x = -12x
-9 + -12x + 5x2 = 24 + 2x + -24 + -2x

Reorder the terms:
-9 + -12x + 5x2 = 24 + -24 + 2x + -2x

Combine like terms: 24 + -24 = 0
-9 + -12x + 5x2 = 0 + 2x + -2x
-9 + -12x + 5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + -12x + 5x2 = 0

Factor a trinomial.
(-3 + -5x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.6, 3}

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