-3x-28=x^2+2x-24

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Solution for -3x-28=x^2+2x-24 equation: 


Simplifying
-3x + -28 = x2 + 2x + -24

Reorder the terms:
-28 + -3x = x2 + 2x + -24

Reorder the terms:
-28 + -3x = -24 + 2x + x2

Solving
-28 + -3x = -24 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-28 + 24 + -3x + -2x + -1x2 = -24 + 2x + x2 + 24 + -2x + -1x2

Combine like terms: -28 + 24 = -4
-4 + -3x + -2x + -1x2 = -24 + 2x + x2 + 24 + -2x + -1x2

Combine like terms: -3x + -2x = -5x
-4 + -5x + -1x2 = -24 + 2x + x2 + 24 + -2x + -1x2

Reorder the terms:
-4 + -5x + -1x2 = -24 + 24 + 2x + -2x + x2 + -1x2

Combine like terms: -24 + 24 = 0
-4 + -5x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-4 + -5x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-4 + -5x + -1x2 = 0 + x2 + -1x2
-4 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5x + x2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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