20x(5x+25)(2x+1)=0

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Solution for 20x(5x+25)(2x+1)=0 equation: 


Simplifying
20x(5x + 25)(2x + 1) = 0

Reorder the terms:
20x(25 + 5x)(2x + 1) = 0

Reorder the terms:
20x(25 + 5x)(1 + 2x) = 0

Multiply (25 + 5x) * (1 + 2x)
20x(25(1 + 2x) + 5x * (1 + 2x)) = 0
20x((1 * 25 + 2x * 25) + 5x * (1 + 2x)) = 0
20x((25 + 50x) + 5x * (1 + 2x)) = 0
20x(25 + 50x + (1 * 5x + 2x * 5x)) = 0
20x(25 + 50x + (5x + 10x2)) = 0

Combine like terms: 50x + 5x = 55x
20x(25 + 55x + 10x2) = 0
(25 * 20x + 55x * 20x + 10x2 * 20x) = 0
(500x + 1100x2 + 200x3) = 0

Solving
500x + 1100x2 + 200x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '100x'.
100x(5 + 11x + 2x2) = 0

Factor a trinomial.
100x((5 + x)(1 + 2x)) = 0

Ignore the factor 100.

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 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -5, -0.5}

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