3x(x+2)-4(x+2)=0

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Solution for 3x(x+2)-4(x+2)=0 equation: 


Simplifying
3x(x + 2) + -4(x + 2) = 0

Reorder the terms:
3x(2 + x) + -4(x + 2) = 0
(2 * 3x + x * 3x) + -4(x + 2) = 0
(6x + 3x2) + -4(x + 2) = 0

Reorder the terms:
6x + 3x2 + -4(2 + x) = 0
6x + 3x2 + (2 * -4 + x * -4) = 0
6x + 3x2 + (-8 + -4x) = 0

Reorder the terms:
-8 + 6x + -4x + 3x2 = 0

Combine like terms: 6x + -4x = 2x
-8 + 2x + 3x2 = 0

Solving
-8 + 2x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(4 + -3x) = 0


Subproblem 1
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

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 = {-2, 1.333333333}

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