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

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


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

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

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

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

Combine like terms: -5x + 3x = -2x
5x(-5 + -2x + 3x2) = 0
(-5 * 5x + -2x * 5x + 3x2 * 5x) = 0
(-25x + -10x2 + 15x3) = 0

Solving
-25x + -10x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-5 + -2x + 3x2) = 0

Factor a trinomial.
5x((-1 + -1x)(5 + -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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -1, 1.666666667}

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