(3x-2)(x+3)-6x=24

Solution for (3x-2)(x+3)-6x=24 equation:

Simplifying
(3x + -2)(x + 3) + -6x = 24

Reorder the terms:
(-2 + 3x)(x + 3) + -6x = 24

Reorder the terms:
(-2 + 3x)(3 + x) + -6x = 24

Multiply (-2 + 3x) * (3 + x)
(-2(3 + x) + 3x * (3 + x)) + -6x = 24
((3 * -2 + x * -2) + 3x * (3 + x)) + -6x = 24
((-6 + -2x) + 3x * (3 + x)) + -6x = 24
(-6 + -2x + (3 * 3x + x * 3x)) + -6x = 24
(-6 + -2x + (9x + 3x2)) + -6x = 24

Combine like terms: -2x + 9x = 7x
(-6 + 7x + 3x2) + -6x = 24

Reorder the terms:
-6 + 7x + -6x + 3x2 = 24

Combine like terms: 7x + -6x = 1x
-6 + 1x + 3x2 = 24

Solving
-6 + 1x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 1x + 3x2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 1x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 1x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.333333333, 3}