5(p+5)(p+2)=0

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Solution for 5(p+5)(p+2)=0 equation: 


Simplifying
5(p + 5)(p + 2) = 0

Reorder the terms:
5(5 + p)(p + 2) = 0

Reorder the terms:
5(5 + p)(2 + p) = 0

Multiply (5 + p) * (2 + p)
5(5(2 + p) + p(2 + p)) = 0
5((2 * 5 + p * 5) + p(2 + p)) = 0
5((10 + 5p) + p(2 + p)) = 0
5(10 + 5p + (2 * p + p * p)) = 0
5(10 + 5p + (2p + p2)) = 0

Combine like terms: 5p + 2p = 7p
5(10 + 7p + p2) = 0
(10 * 5 + 7p * 5 + p2 * 5) = 0
(50 + 35p + 5p2) = 0

Solving
50 + 35p + 5p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + 7p + p2) = 0

Factor a trinomial.
5((5 + p)(2 + p)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 0

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

Add '-5' to each side of the equation.
5 + -5 + p = 0 + -5

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

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

Simplifying
p = -5

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2
Solution
p = {-5, -2}

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