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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Ignore the factor 3.
Subproblem 1
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 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.2, 4}