(2x+1)(3x-5)x=0

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Solution for (2x+1)(3x-5)x=0 equation: 


Simplifying
(2x + 1)(3x + -5) * x = 0

Reorder the terms:
(1 + 2x)(3x + -5) * x = 0

Reorder the terms:
(1 + 2x)(-5 + 3x) * x = 0

Reorder the terms for easier multiplication:
x(1 + 2x)(-5 + 3x) = 0

Multiply (1 + 2x) * (-5 + 3x)
x(1(-5 + 3x) + 2x * (-5 + 3x)) = 0
x((-5 * 1 + 3x * 1) + 2x * (-5 + 3x)) = 0
x((-5 + 3x) + 2x * (-5 + 3x)) = 0
x(-5 + 3x + (-5 * 2x + 3x * 2x)) = 0
x(-5 + 3x + (-10x + 6x2)) = 0

Combine like terms: 3x + -10x = -7x
x(-5 + -7x + 6x2) = 0
(-5 * x + -7x * x + 6x2 * x) = 0
(-5x + -7x2 + 6x3) = 0

Solving
-5x + -7x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + -7x + 6x2) = 0

Factor a trinomial.
x((-1 + -2x)(5 + -3x)) = 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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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, -0.5, 1.666666667}

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