3x^2-x-24=x(2x-3)

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Solution for 3x^2-x-24=x(2x-3) equation: 


Simplifying
3x2 + -1x + -24 = x(2x + -3)

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

Reorder the terms:
-24 + -1x + 3x2 = x(-3 + 2x)
-24 + -1x + 3x2 = (-3 * x + 2x * x)
-24 + -1x + 3x2 = (-3x + 2x2)

Solving
-24 + -1x + 3x2 = -3x + 2x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: -3x + 3x = 0
-24 + 2x + 1x2 = 0 + 2x2 + -2x2
-24 + 2x + 1x2 = 2x2 + -2x2

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

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6, 4}

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