2x^2-37x=5x^2-3x-24

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Solution for 2x^2-37x=5x^2-3x-24 equation: 


Simplifying
2x2 + -37x = 5x2 + -3x + -24

Reorder the terms:
-37x + 2x2 = 5x2 + -3x + -24

Reorder the terms:
-37x + 2x2 = -24 + -3x + 5x2

Solving
-37x + 2x2 = -24 + -3x + 5x2

Solving for variable 'x'.

Reorder the terms:
24 + -37x + 3x + 2x2 + -5x2 = -24 + -3x + 5x2 + 24 + 3x + -5x2

Combine like terms: -37x + 3x = -34x
24 + -34x + 2x2 + -5x2 = -24 + -3x + 5x2 + 24 + 3x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
24 + -34x + -3x2 = -24 + -3x + 5x2 + 24 + 3x + -5x2

Reorder the terms:
24 + -34x + -3x2 = -24 + 24 + -3x + 3x + 5x2 + -5x2

Combine like terms: -24 + 24 = 0
24 + -34x + -3x2 = 0 + -3x + 3x + 5x2 + -5x2
24 + -34x + -3x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
24 + -34x + -3x2 = 0 + 5x2 + -5x2
24 + -34x + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
24 + -34x + -3x2 = 0

Factor a trinomial.
(2 + -3x)(12 + x) = 0


Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {0.6666666667, -12}

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