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

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

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

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

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

Combine like terms: 1x + -15x = -14x
4x(-3 + -14x + 5x2) = 0
(-3 * 4x + -14x * 4x + 5x2 * 4x) = 0
(-12x + -56x2 + 20x3) = 0

Solving
-12x + -56x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-3 + -14x + 5x2) = 0

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

Ignore the factor 4.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -0.2, 3}