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

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


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

Combine like terms: 2 + 2 = 4
3x(4) = x(3x + -2) + -24

Reorder the terms for easier multiplication:
3 * 4x = x(3x + -2) + -24

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

Reorder the terms:
12x = x(-2 + 3x) + -24
12x = (-2 * x + 3x * x) + -24
12x = (-2x + 3x2) + -24

Reorder the terms:
12x = -24 + -2x + 3x2

Solving
12x = -24 + -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
24 + 12x + 2x + -3x2 = -24 + -2x + 3x2 + 24 + 2x + -3x2

Combine like terms: 12x + 2x = 14x
24 + 14x + -3x2 = -24 + -2x + 3x2 + 24 + 2x + -3x2

Reorder the terms:
24 + 14x + -3x2 = -24 + 24 + -2x + 2x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
24 + 14x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
24 + 14x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
24 + 14x + -3x2 = 0 + 3x2 + -3x2
24 + 14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + 14x + -3x2 = 0

Factor a trinomial.
(6 + -1x)(4 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {6, -1.333333333}

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