x(2x+4)(2x-5)=0

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Solution for x(2x+4)(2x-5)=0 equation: 


Simplifying
x(2x + 4)(2x + -5) = 0

Reorder the terms:
x(4 + 2x)(2x + -5) = 0

Reorder the terms:
x(4 + 2x)(-5 + 2x) = 0

Multiply (4 + 2x) * (-5 + 2x)
x(4(-5 + 2x) + 2x * (-5 + 2x)) = 0
x((-5 * 4 + 2x * 4) + 2x * (-5 + 2x)) = 0
x((-20 + 8x) + 2x * (-5 + 2x)) = 0
x(-20 + 8x + (-5 * 2x + 2x * 2x)) = 0
x(-20 + 8x + (-10x + 4x2)) = 0

Combine like terms: 8x + -10x = -2x
x(-20 + -2x + 4x2) = 0
(-20 * x + -2x * x + 4x2 * x) = 0
(-20x + -2x2 + 4x3) = 0

Solving
-20x + -2x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-10 + -1x + 2x2) = 0

Factor a trinomial.
2x((-2 + -1x)(5 + -2x)) = 0

Ignore the factor 2.

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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