-5(p+2)=2(2p-15)p

Solution for -5(p+2)=2(2p-15)p equation:

Simplifying
-5(p + 2) = 2(2p + -15) * p

Reorder the terms:
-5(2 + p) = 2(2p + -15) * p
(2 * -5 + p * -5) = 2(2p + -15) * p
(-10 + -5p) = 2(2p + -15) * p

Reorder the terms:
-10 + -5p = 2(-15 + 2p) * p

Reorder the terms for easier multiplication:
-10 + -5p = 2p(-15 + 2p)
-10 + -5p = (-15 * 2p + 2p * 2p)
-10 + -5p = (-30p + 4p2)

Solving
-10 + -5p = -30p + 4p2

Solving for variable 'p'.

Combine like terms: -5p + 30p = 25p
-10 + 25p + -4p2 = -30p + 4p2 + 30p + -4p2

Reorder the terms:
-10 + 25p + -4p2 = -30p + 30p + 4p2 + -4p2

Combine like terms: -30p + 30p = 0
-10 + 25p + -4p2 = 0 + 4p2 + -4p2
-10 + 25p + -4p2 = 4p2 + -4p2

Combine like terms: 4p2 + -4p2 = 0
-10 + 25p + -4p2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
2.5 + -6.25p + p2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6.25p + -2.5 + p2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6.25p + p2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6.25p + p2 = 0 + -2.5
-6.25p + p2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6.25p + p2 = -2.5

The p term is -6.25p.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25p + 9.765625 + p2 = -2.5 + 9.765625

Reorder the terms:
9.765625 + -6.25p + p2 = -2.5 + 9.765625

Combine like terms: -2.5 + 9.765625 = 7.265625
9.765625 + -6.25p + p2 = 7.265625

Factor a perfect square on the left side:
(p + -3.125)(p + -3.125) = 7.265625

Calculate the square root of the right side: 2.695482332

Break this problem into two subproblems by setting 
(p + -3.125) equal to 2.695482332 and -2.695482332.

Subproblem 1
p + -3.125 = 2.695482332

Simplifying
p + -3.125 = 2.695482332

Reorder the terms:
-3.125 + p = 2.695482332

Solving
-3.125 + p = 2.695482332

Solving for variable 'p'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + p = 2.695482332 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + p = 2.695482332 + 3.125
p = 2.695482332 + 3.125

Combine like terms: 2.695482332 + 3.125 = 5.820482332
p = 5.820482332

Simplifying
p = 5.820482332

Subproblem 2
p + -3.125 = -2.695482332

Simplifying
p + -3.125 = -2.695482332

Reorder the terms:
-3.125 + p = -2.695482332

Solving
-3.125 + p = -2.695482332

Solving for variable 'p'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + p = -2.695482332 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + p = -2.695482332 + 3.125
p = -2.695482332 + 3.125

Combine like terms: -2.695482332 + 3.125 = 0.429517668
p = 0.429517668

Simplifying
p = 0.429517668

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.820482332, 0.429517668}