(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 = -120p
(200 + -120p + 10p2) = 0

Solving
200 + -120p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '10'.
10(20 + -12p + p2) = 0

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

Ignore the factor 10.

Subproblem 1
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

Subproblem 2
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
Solution
p = {2, 10}

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