3x(5x+1)(4x-3)=0

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Solution for 3x(5x+1)(4x-3)=0 equation: 


Simplifying
3x(5x + 1)(4x + -3) = 0

Reorder the terms:
3x(1 + 5x)(4x + -3) = 0

Reorder the terms:
3x(1 + 5x)(-3 + 4x) = 0

Multiply (1 + 5x) * (-3 + 4x)
3x(1(-3 + 4x) + 5x * (-3 + 4x)) = 0
3x((-3 * 1 + 4x * 1) + 5x * (-3 + 4x)) = 0
3x((-3 + 4x) + 5x * (-3 + 4x)) = 0
3x(-3 + 4x + (-3 * 5x + 4x * 5x)) = 0
3x(-3 + 4x + (-15x + 20x2)) = 0

Combine like terms: 4x + -15x = -11x
3x(-3 + -11x + 20x2) = 0
(-3 * 3x + -11x * 3x + 20x2 * 3x) = 0
(-9x + -33x2 + 60x3) = 0

Solving
-9x + -33x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-3 + -11x + 20x2) = 0

Factor a trinomial.
3x((-1 + -5x)(3 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

Subproblem 3
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, -0.2, 0.75}

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