x(4x+1)(x-6)=0

Solution for x(4x+1)(x-6)=0 equation:

Simplifying
x(4x + 1)(x + -6) = 0

Reorder the terms:
x(1 + 4x)(x + -6) = 0

Reorder the terms:
x(1 + 4x)(-6 + x) = 0

Multiply (1 + 4x) * (-6 + x)
x(1(-6 + x) + 4x * (-6 + x)) = 0
x((-6 * 1 + x * 1) + 4x * (-6 + x)) = 0
x((-6 + 1x) + 4x * (-6 + x)) = 0
x(-6 + 1x + (-6 * 4x + x * 4x)) = 0
x(-6 + 1x + (-24x + 4x2)) = 0

Combine like terms: 1x + -24x = -23x
x(-6 + -23x + 4x2) = 0
(-6 * x + -23x * x + 4x2 * x) = 0
(-6x + -23x2 + 4x3) = 0

Solving
-6x + -23x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -23x + 4x2) = 0

Factor a trinomial.
x((-1 + -4x)(6 + -1x)) = 0

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -0.25, 6}