3(5x-4)(3x+2)=0

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Solution for 3(5x-4)(3x+2)=0 equation: 


Simplifying
3(5x + -4)(3x + 2) = 0

Reorder the terms:
3(-4 + 5x)(3x + 2) = 0

Reorder the terms:
3(-4 + 5x)(2 + 3x) = 0

Multiply (-4 + 5x) * (2 + 3x)
3(-4(2 + 3x) + 5x * (2 + 3x)) = 0
3((2 * -4 + 3x * -4) + 5x * (2 + 3x)) = 0
3((-8 + -12x) + 5x * (2 + 3x)) = 0
3(-8 + -12x + (2 * 5x + 3x * 5x)) = 0
3(-8 + -12x + (10x + 15x2)) = 0

Combine like terms: -12x + 10x = -2x
3(-8 + -2x + 15x2) = 0
(-8 * 3 + -2x * 3 + 15x2 * 3) = 0
(-24 + -6x + 45x2) = 0

Solving
-24 + -6x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2x + 15x2) = 0

Factor a trinomial.
3((-2 + -3x)(4 + -5x)) = 0

Ignore the factor 3.

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 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-0.6666666667, 0.8}

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