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

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


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

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

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

Multiply (5 + 2x) * (-5 + 2x)
3x(5(-5 + 2x) + 2x * (-5 + 2x)) = 0
3x((-5 * 5 + 2x * 5) + 2x * (-5 + 2x)) = 0
3x((-25 + 10x) + 2x * (-5 + 2x)) = 0
3x(-25 + 10x + (-5 * 2x + 2x * 2x)) = 0
3x(-25 + 10x + (-10x + 4x2)) = 0

Combine like terms: 10x + -10x = 0
3x(-25 + 0 + 4x2) = 0
3x(-25 + 4x2) = 0
(-25 * 3x + 4x2 * 3x) = 0
(-75x + 12x3) = 0

Solving
-75x + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-25 + 4x2) = 0

Factor a difference between two squares.
3x((5 + 2x)(-5 + 2x)) = 0

Ignore the factor 3.

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 '(-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, -2.5, 2.5}

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