3p-16=p(p-7)

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Solution for 3p-16=p(p-7) equation: 


Simplifying
3p + -16 = p(p + -7)

Reorder the terms:
-16 + 3p = p(p + -7)

Reorder the terms:
-16 + 3p = p(-7 + p)
-16 + 3p = (-7 * p + p * p)
-16 + 3p = (-7p + p2)

Solving
-16 + 3p = -7p + p2

Solving for variable 'p'.

Combine like terms: 3p + 7p = 10p
-16 + 10p + -1p2 = -7p + p2 + 7p + -1p2

Reorder the terms:
-16 + 10p + -1p2 = -7p + 7p + p2 + -1p2

Combine like terms: -7p + 7p = 0
-16 + 10p + -1p2 = 0 + p2 + -1p2
-16 + 10p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-16 + 10p + -1p2 = 0

Factor a trinomial.
(-8 + p)(2 + -1p) = 0


Subproblem 1
Set the factor '(-8 + p)' equal to zero and attempt to solve:

Simplifying
-8 + p = 0

Solving
-8 + p = 0

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

Add '8' to each side of the equation.
-8 + 8 + p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + p = 0 + 8
p = 0 + 8

Combine like terms: 0 + 8 = 8
p = 8

Simplifying
p = 8

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 = {8, 2}

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