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

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


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

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

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

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

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

Solving
-5x + -3x2 + 2x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((-1 + -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 '(-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 + -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, -1, 2.5}

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