(2x^2)(2x+5)(x+5)=0

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


Simplifying
(2x2)(2x + 5)(x + 5) = 0

Remove parenthesis around (2x2)
2x2(2x + 5)(x + 5) = 0

Reorder the terms:
2x2(5 + 2x)(x + 5) = 0

Reorder the terms:
2x2(5 + 2x)(5 + x) = 0

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

Combine like terms: 5x + 10x = 15x
2x2(25 + 15x + 2x2) = 0
(25 * 2x2 + 15x * 2x2 + 2x2 * 2x2) = 0
(50x2 + 30x3 + 4x4) = 0

Solving
50x2 + 30x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(25 + 15x + 2x2) = 0

Factor a trinomial.
2x2((5 + x)(5 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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 '(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, -5, -2.5}

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