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

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


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

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

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

Multiply (4 + x) * (1 + 3x)
0 = 5x(4(1 + 3x) + x(1 + 3x))
0 = 5x((1 * 4 + 3x * 4) + x(1 + 3x))
0 = 5x((4 + 12x) + x(1 + 3x))
0 = 5x(4 + 12x + (1 * x + 3x * x))
0 = 5x(4 + 12x + (1x + 3x2))

Combine like terms: 12x + 1x = 13x
0 = 5x(4 + 13x + 3x2)
0 = (4 * 5x + 13x * 5x + 3x2 * 5x)
0 = (20x + 65x2 + 15x3)

Solving
0 = 20x + 65x2 + 15x3

Solving for variable 'x'.
Remove the zero:
-20x + -65x2 + -15x3 = 20x + 65x2 + 15x3 + -20x + -65x2 + -15x3

Reorder the terms:
-20x + -65x2 + -15x3 = 20x + -20x + 65x2 + -65x2 + 15x3 + -15x3

Combine like terms: 20x + -20x = 0
-20x + -65x2 + -15x3 = 0 + 65x2 + -65x2 + 15x3 + -15x3
-20x + -65x2 + -15x3 = 65x2 + -65x2 + 15x3 + -15x3

Combine like terms: 65x2 + -65x2 = 0
-20x + -65x2 + -15x3 = 0 + 15x3 + -15x3
-20x + -65x2 + -15x3 = 15x3 + -15x3

Combine like terms: 15x3 + -15x3 = 0
-20x + -65x2 + -15x3 = 0

Factor out the Greatest Common Factor (GCF), '-5x'.
-5x(4 + 13x + 3x2) = 0

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

Ignore the factor -5.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4

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

Simplifying
1 + 3x = 0

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0, -4, -0.3333333333}

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