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

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


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

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

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

Multiply (4 + 5x) * (3 + x)
x(4(3 + x) + 5x * (3 + x)) = 0
x((3 * 4 + x * 4) + 5x * (3 + x)) = 0
x((12 + 4x) + 5x * (3 + x)) = 0
x(12 + 4x + (3 * 5x + x * 5x)) = 0
x(12 + 4x + (15x + 5x2)) = 0

Combine like terms: 4x + 15x = 19x
x(12 + 19x + 5x2) = 0
(12 * x + 19x * x + 5x2 * x) = 0
(12x + 19x2 + 5x3) = 0

Solving
12x + 19x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + 19x + 5x2) = 0

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

Subproblem 3
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 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 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {0, -3, -0.8}

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