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

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


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

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

Multiply (4 + -3x) * (4 + 5x)
3(4(4 + 5x) + -3x * (4 + 5x)) = 0
3((4 * 4 + 5x * 4) + -3x * (4 + 5x)) = 0
3((16 + 20x) + -3x * (4 + 5x)) = 0
3(16 + 20x + (4 * -3x + 5x * -3x)) = 0
3(16 + 20x + (-12x + -15x2)) = 0

Combine like terms: 20x + -12x = 8x
3(16 + 8x + -15x2) = 0
(16 * 3 + 8x * 3 + -15x2 * 3) = 0
(48 + 24x + -45x2) = 0

Solving
48 + 24x + -45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 8x + -15x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {1.333333333, -0.8}

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