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

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


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

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

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

Multiply (2 + 3x) * (-4 + 3x)
(2(-4 + 3x) + 3x * (-4 + 3x)) = 0
((-4 * 2 + 3x * 2) + 3x * (-4 + 3x)) = 0
((-8 + 6x) + 3x * (-4 + 3x)) = 0
(-8 + 6x + (-4 * 3x + 3x * 3x)) = 0
(-8 + 6x + (-12x + 9x2)) = 0

Combine like terms: 6x + -12x = -6x
(-8 + -6x + 9x2) = 0

Solving
-8 + -6x + 9x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, 1.333333333}

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