(5p-10)(2p+20)=0

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Solution for (5p-10)(2p+20)=0 equation: 


Simplifying
(5p + -10)(2p + 20) = 0

Reorder the terms:
(-10 + 5p)(2p + 20) = 0

Reorder the terms:
(-10 + 5p)(20 + 2p) = 0

Multiply (-10 + 5p) * (20 + 2p)
(-10(20 + 2p) + 5p * (20 + 2p)) = 0
((20 * -10 + 2p * -10) + 5p * (20 + 2p)) = 0
((-200 + -20p) + 5p * (20 + 2p)) = 0
(-200 + -20p + (20 * 5p + 2p * 5p)) = 0
(-200 + -20p + (100p + 10p2)) = 0

Combine like terms: -20p + 100p = 80p
(-200 + 80p + 10p2) = 0

Solving
-200 + 80p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-20 + 8p + p2) = 0

Factor a trinomial.
10((-10 + -1p)(2 + -1p)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-10 + -1p)' equal to zero and attempt to solve:

Simplifying
-10 + -1p = 0

Solving
-10 + -1p = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1p = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1p = 0 + 10
-1p = 0 + 10

Combine like terms: 0 + 10 = 10
-1p = 10

Divide each side by '-1'.
p = -10

Simplifying
p = -10

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

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

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

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

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-10, 2}

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