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

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


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

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

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

Multiply (-5 + 2x) * (-2 + x)
x(-5(-2 + x) + 2x * (-2 + x)) = 0
x((-2 * -5 + x * -5) + 2x * (-2 + x)) = 0
x((10 + -5x) + 2x * (-2 + x)) = 0
x(10 + -5x + (-2 * 2x + x * 2x)) = 0
x(10 + -5x + (-4x + 2x2)) = 0

Combine like terms: -5x + -4x = -9x
x(10 + -9x + 2x2) = 0
(10 * x + -9x * x + 2x2 * x) = 0
(10x + -9x2 + 2x3) = 0

Solving
10x + -9x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -9x + 2x2) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
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
Solution
x = {0, 2, 2.5}

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