p^2+100-20p=3p(p-1)

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Solution for p^2+100-20p=3p(p-1) equation: 


Simplifying
p2 + 100 + -20p = 3p(p + -1)

Reorder the terms:
100 + -20p + p2 = 3p(p + -1)

Reorder the terms:
100 + -20p + p2 = 3p(-1 + p)
100 + -20p + p2 = (-1 * 3p + p * 3p)
100 + -20p + p2 = (-3p + 3p2)

Solving
100 + -20p + p2 = -3p + 3p2

Solving for variable 'p'.

Reorder the terms:
100 + -20p + 3p + p2 + -3p2 = -3p + 3p2 + 3p + -3p2

Combine like terms: -20p + 3p = -17p
100 + -17p + p2 + -3p2 = -3p + 3p2 + 3p + -3p2

Combine like terms: p2 + -3p2 = -2p2
100 + -17p + -2p2 = -3p + 3p2 + 3p + -3p2

Reorder the terms:
100 + -17p + -2p2 = -3p + 3p + 3p2 + -3p2

Combine like terms: -3p + 3p = 0
100 + -17p + -2p2 = 0 + 3p2 + -3p2
100 + -17p + -2p2 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
100 + -17p + -2p2 = 0

Factor a trinomial.
(4 + -1p)(25 + 2p) = 0


Subproblem 1
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4

Subproblem 2
Set the factor '(25 + 2p)' equal to zero and attempt to solve:

Simplifying
25 + 2p = 0

Solving
25 + 2p = 0

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

Add '-25' to each side of the equation.
25 + -25 + 2p = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 2p = 0 + -25
2p = 0 + -25

Combine like terms: 0 + -25 = -25
2p = -25

Divide each side by '2'.
p = -12.5

Simplifying
p = -12.5
Solution
p = {4, -12.5}

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