1.5=-2p^2+4p

Solution for 1.5=-2p^2+4p equation:

Simplifying
1.5 = -2p2 + 4p

Reorder the terms:
1.5 = 4p + -2p2

Solving
1.5 = 4p + -2p2

Solving for variable 'p'.

Reorder the terms:
1.5 + -4p + 2p2 = 4p + -4p + -2p2 + 2p2

Combine like terms: 4p + -4p = 0
1.5 + -4p + 2p2 = 0 + -2p2 + 2p2
1.5 + -4p + 2p2 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
1.5 + -4p + 2p2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.75 + -2p + p2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2p + -0.75 + p2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2p + p2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2p + p2 = 0 + -0.75
-2p + p2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2p + p2 = -0.75

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = -0.75 + 1

Reorder the terms:
1 + -2p + p2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2p + p2 = 0.25

Factor a perfect square on the left side:
(p + -1)(p + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(p + -1) equal to 0.5 and -0.5.

Subproblem 1
p + -1 = 0.5

Simplifying
p + -1 = 0.5

Reorder the terms:
-1 + p = 0.5

Solving
-1 + p = 0.5

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 0.5 + 1

Combine like terms: -1 + 1 = 0
0 + p = 0.5 + 1
p = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
p = 1.5

Simplifying
p = 1.5

Subproblem 2
p + -1 = -0.5

Simplifying
p + -1 = -0.5

Reorder the terms:
-1 + p = -0.5

Solving
-1 + p = -0.5

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -0.5 + 1

Combine like terms: -1 + 1 = 0
0 + p = -0.5 + 1
p = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
p = 0.5

Simplifying
p = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.5, 0.5}