(3x-2)(x+4)=24

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Solution for (3x-2)(x+4)=24 equation: 


Simplifying
(3x + -2)(x + 4) = 24

Reorder the terms:
(-2 + 3x)(x + 4) = 24

Reorder the terms:
(-2 + 3x)(4 + x) = 24

Multiply (-2 + 3x) * (4 + x)
(-2(4 + x) + 3x * (4 + x)) = 24
((4 * -2 + x * -2) + 3x * (4 + x)) = 24
((-8 + -2x) + 3x * (4 + x)) = 24
(-8 + -2x + (4 * 3x + x * 3x)) = 24
(-8 + -2x + (12x + 3x2)) = 24

Combine like terms: -2x + 12x = 10x
(-8 + 10x + 3x2) = 24

Solving
-8 + 10x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-8 + -24 + 10x + 3x2 = 24 + -24

Combine like terms: -8 + -24 = -32
-32 + 10x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-32 + 10x + 3x2 = 0

Factor a trinomial.
(-16 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-16 + -3x)' equal to zero and attempt to solve:

Simplifying
-16 + -3x = 0

Solving
-16 + -3x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3x = 0 + 16
-3x = 0 + 16

Combine like terms: 0 + 16 = 16
-3x = 16

Divide each side by '-3'.
x = -5.333333333

Simplifying
x = -5.333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5.333333333, 2}

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