2x^2+2x+24=x^2-6x+9

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Solution for 2x^2+2x+24=x^2-6x+9 equation: 


Simplifying
2x2 + 2x + 24 = x2 + -6x + 9

Reorder the terms:
24 + 2x + 2x2 = x2 + -6x + 9

Reorder the terms:
24 + 2x + 2x2 = 9 + -6x + x2

Solving
24 + 2x + 2x2 = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
24 + -9 + 2x + 6x + 2x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 24 + -9 = 15
15 + 2x + 6x + 2x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 2x + 6x = 8x
15 + 8x + 2x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
15 + 8x + 1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
15 + 8x + 1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
15 + 8x + 1x2 = 0 + -6x + 6x + x2 + -1x2
15 + 8x + 1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
15 + 8x + 1x2 = 0 + x2 + -1x2
15 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 1x2 = 0

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


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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-5, -3}

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