p^2=2(1.5-p)

Solution for p^2=2(1.5-p) equation:

Simplifying
p2 = 2(1.5 + -1p)
p2 = (1.5 * 2 + -1p * 2)
p2 = (3 + -2p)

Solving
p2 = 3 + -2p

Solving for variable 'p'.

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

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

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

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

Factor a trinomial.
(-3 + -1p)(1 + -1p) = 0

Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3

Combine like terms: 0 + 3 = 3
-1p = 3

Divide each side by '-1'.
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

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

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

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

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

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

Simplifying
p = 1
Solution
p = {-3, 1}