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Simplifying
p2 + 21p + -49 = 21p

Reorder the terms:
-49 + 21p + p2 = 21p

Add '-21p' to each side of the equation.
-49 + 21p + -21p + p2 = 21p + -21p

Combine like terms: 21p + -21p = 0
-49 + 0 + p2 = 21p + -21p
-49 + p2 = 21p + -21p

Combine like terms: 21p + -21p = 0
-49 + p2 = 0

Solving
-49 + p2 = 0

Solving for variable 'p'.

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

Add '49' to each side of the equation.
-49 + 49 + p2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + p2 = 0 + 49
p2 = 0 + 49

Combine like terms: 0 + 49 = 49
p2 = 49

Simplifying
p2 = 49

Reorder the terms:
-49 + p2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + p2 = 0

Factor a difference between two squares.
(7 + p)(-7 + p) = 0

Subproblem 1

Set the factor '(7 + p)' equal to zero and attempt to solve: Simplifying 7 + p = 0 Solving 7 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + p = 0 + -7 p = 0 + -7 Combine like terms: 0 + -7 = -7 p = -7 Simplifying p = -7

Subproblem 2

Set the factor '(-7 + p)' equal to zero and attempt to solve: Simplifying -7 + p = 0 Solving -7 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + p = 0 + 7 p = 0 + 7 Combine like terms: 0 + 7 = 7 p = 7 Simplifying p = 7

Solution

p = {-7, 7}
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