9-24x=-11x+45+x^2

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Solution for 9-24x=-11x+45+x^2 equation: 


Simplifying
9 + -24x = -11x + 45 + x2

Reorder the terms:
9 + -24x = 45 + -11x + x2

Solving
9 + -24x = 45 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -45 + -24x + 11x + -1x2 = 45 + -11x + x2 + -45 + 11x + -1x2

Combine like terms: 9 + -45 = -36
-36 + -24x + 11x + -1x2 = 45 + -11x + x2 + -45 + 11x + -1x2

Combine like terms: -24x + 11x = -13x
-36 + -13x + -1x2 = 45 + -11x + x2 + -45 + 11x + -1x2

Reorder the terms:
-36 + -13x + -1x2 = 45 + -45 + -11x + 11x + x2 + -1x2

Combine like terms: 45 + -45 = 0
-36 + -13x + -1x2 = 0 + -11x + 11x + x2 + -1x2
-36 + -13x + -1x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
-36 + -13x + -1x2 = 0 + x2 + -1x2
-36 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 13x + x2) = 0

Factor a trinomial.
-1((9 + x)(4 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-9, -4}

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