3x^2+23x=5x-24

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Solution for 3x^2+23x=5x-24 equation: 


Simplifying
3x2 + 23x = 5x + -24

Reorder the terms:
23x + 3x2 = 5x + -24

Reorder the terms:
23x + 3x2 = -24 + 5x

Solving
23x + 3x2 = -24 + 5x

Solving for variable 'x'.

Reorder the terms:
24 + 23x + -5x + 3x2 = -24 + 5x + 24 + -5x

Combine like terms: 23x + -5x = 18x
24 + 18x + 3x2 = -24 + 5x + 24 + -5x

Reorder the terms:
24 + 18x + 3x2 = -24 + 24 + 5x + -5x

Combine like terms: -24 + 24 = 0
24 + 18x + 3x2 = 0 + 5x + -5x
24 + 18x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
24 + 18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 6x + x2) = 0

Factor a trinomial.
3((4 + x)(2 + x)) = 0

Ignore the factor 3.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-4, -2}

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