2(1-p^2)=3(p-6)

Solution for 2(1-p^2)=3(p-6) equation:

Simplifying
2(1 + -1p2) = 3(p + -6)
(1 * 2 + -1p2 * 2) = 3(p + -6)
(2 + -2p2) = 3(p + -6)

Reorder the terms:
2 + -2p2 = 3(-6 + p)
2 + -2p2 = (-6 * 3 + p * 3)
2 + -2p2 = (-18 + 3p)

Solving
2 + -2p2 = -18 + 3p

Solving for variable 'p'.

Reorder the terms:
2 + 18 + -3p + -2p2 = -18 + 3p + 18 + -3p

Combine like terms: 2 + 18 = 20
20 + -3p + -2p2 = -18 + 3p + 18 + -3p

Reorder the terms:
20 + -3p + -2p2 = -18 + 18 + 3p + -3p

Combine like terms: -18 + 18 = 0
20 + -3p + -2p2 = 0 + 3p + -3p
20 + -3p + -2p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
20 + -3p + -2p2 = 0

Factor a trinomial.
(5 + -2p)(4 + p) = 0

Subproblem 1
Set the factor '(5 + -2p)' equal to zero and attempt to solve:

Simplifying
5 + -2p = 0

Solving
5 + -2p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2p = 0 + -5
-2p = 0 + -5

Combine like terms: 0 + -5 = -5
-2p = -5

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 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 + p = 0 + -4

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

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

Simplifying
p = -4
Solution
p = {2.5, -4}