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

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

Simplifying
(5x + 3) * x(x + -3) = 0

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

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

Reorder the terms for easier multiplication:
x(3 + 5x)(-3 + x) = 0

Multiply (3 + 5x) * (-3 + x)
x(3(-3 + x) + 5x * (-3 + x)) = 0
x((-3 * 3 + x * 3) + 5x * (-3 + x)) = 0
x((-9 + 3x) + 5x * (-3 + x)) = 0
x(-9 + 3x + (-3 * 5x + x * 5x)) = 0
x(-9 + 3x + (-15x + 5x2)) = 0

Combine like terms: 3x + -15x = -12x
x(-9 + -12x + 5x2) = 0
(-9 * x + -12x * x + 5x2 * x) = 0
(-9x + -12x2 + 5x3) = 0

Solving
-9x + -12x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + -12x + 5x2) = 0

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

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6
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, -0.6, 3}