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

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


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

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

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

Multiply (-3 + x) * (-5 + 2x)
x(-3(-5 + 2x) + x(-5 + 2x)) = 0
x((-5 * -3 + 2x * -3) + x(-5 + 2x)) = 0
x((15 + -6x) + x(-5 + 2x)) = 0
x(15 + -6x + (-5 * x + 2x * x)) = 0
x(15 + -6x + (-5x + 2x2)) = 0

Combine like terms: -6x + -5x = -11x
x(15 + -11x + 2x2) = 0
(15 * x + -11x * x + 2x2 * x) = 0
(15x + -11x2 + 2x3) = 0

Solving
15x + -11x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -11x + 2x2) = 0

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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, 2.5, 3}

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