2x^2-28x=3x^2-5x-24

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Solution for 2x^2-28x=3x^2-5x-24 equation: 


Simplifying
2x2 + -28x = 3x2 + -5x + -24

Reorder the terms:
-28x + 2x2 = 3x2 + -5x + -24

Reorder the terms:
-28x + 2x2 = -24 + -5x + 3x2

Solving
-28x + 2x2 = -24 + -5x + 3x2

Solving for variable 'x'.

Reorder the terms:
24 + -28x + 5x + 2x2 + -3x2 = -24 + -5x + 3x2 + 24 + 5x + -3x2

Combine like terms: -28x + 5x = -23x
24 + -23x + 2x2 + -3x2 = -24 + -5x + 3x2 + 24 + 5x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
24 + -23x + -1x2 = -24 + -5x + 3x2 + 24 + 5x + -3x2

Reorder the terms:
24 + -23x + -1x2 = -24 + 24 + -5x + 5x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
24 + -23x + -1x2 = 0 + -5x + 5x + 3x2 + -3x2
24 + -23x + -1x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
24 + -23x + -1x2 = 0 + 3x2 + -3x2
24 + -23x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + -23x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(24 + x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(24 + x)' equal to zero and attempt to solve:

Simplifying
24 + x = 0

Solving
24 + x = 0

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

Add '-24' to each side of the equation.
24 + -24 + x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + x = 0 + -24
x = 0 + -24

Combine like terms: 0 + -24 = -24
x = -24

Simplifying
x = -24
Solution
x = {1, -24}

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