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

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


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

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

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

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

Combine like terms: 1x + -20x = -19x
3x(-5 + -19x + 4x2) = 0
(-5 * 3x + -19x * 3x + 4x2 * 3x) = 0
(-15x + -57x2 + 12x3) = 0

Solving
-15x + -57x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + -19x + 4x2) = 0

Factor a trinomial.
3x((-1 + -4x)(5 + -1x)) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -0.25, 5}

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