(2p^2-7p-30)=p-6

Solution for (2p^2-7p-30)=p-6 equation:

Simplifying
(2p2 + -7p + -30) = p + -6

Reorder the terms:
(-30 + -7p + 2p2) = p + -6

Remove parenthesis around (-30 + -7p + 2p2)
-30 + -7p + 2p2 = p + -6

Reorder the terms:
-30 + -7p + 2p2 = -6 + p

Solving
-30 + -7p + 2p2 = -6 + p

Solving for variable 'p'.

Reorder the terms:
-30 + 6 + -7p + -1p + 2p2 = -6 + p + 6 + -1p

Combine like terms: -30 + 6 = -24
-24 + -7p + -1p + 2p2 = -6 + p + 6 + -1p

Combine like terms: -7p + -1p = -8p
-24 + -8p + 2p2 = -6 + p + 6 + -1p

Reorder the terms:
-24 + -8p + 2p2 = -6 + 6 + p + -1p

Combine like terms: -6 + 6 = 0
-24 + -8p + 2p2 = 0 + p + -1p
-24 + -8p + 2p2 = p + -1p

Combine like terms: p + -1p = 0
-24 + -8p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -4p + p2) = 0

Factor a trinomial.
2((-2 + -1p)(6 + -1p)) = 0

Ignore the factor 2.
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 '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {-2, 6}