4p(p-15)=6(10-p)+4p

Solution for 4p(p-15)=6(10-p)+4p equation:

Simplifying
4p(p + -15) = 6(10 + -1p) + 4p

Reorder the terms:
4p(-15 + p) = 6(10 + -1p) + 4p
(-15 * 4p + p * 4p) = 6(10 + -1p) + 4p
(-60p + 4p2) = 6(10 + -1p) + 4p
-60p + 4p2 = (10 * 6 + -1p * 6) + 4p
-60p + 4p2 = (60 + -6p) + 4p

Combine like terms: -6p + 4p = -2p
-60p + 4p2 = 60 + -2p

Solving
-60p + 4p2 = 60 + -2p

Solving for variable 'p'.

Reorder the terms:
-60 + -60p + 2p + 4p2 = 60 + -2p + -60 + 2p

Combine like terms: -60p + 2p = -58p
-60 + -58p + 4p2 = 60 + -2p + -60 + 2p

Reorder the terms:
-60 + -58p + 4p2 = 60 + -60 + -2p + 2p

Combine like terms: 60 + -60 = 0
-60 + -58p + 4p2 = 0 + -2p + 2p
-60 + -58p + 4p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
-60 + -58p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -29p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + -29p + 2p2)' equal to zero and attempt to solve:

Simplifying
-30 + -29p + 2p2 = 0

Solving
-30 + -29p + 2p2 = 0

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

Divide each side by '2'.
-15 + -14.5p + p2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -14.5p + 15 + p2 = 0 + 15

Reorder the terms:
-15 + 15 + -14.5p + p2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -14.5p + p2 = 0 + 15
-14.5p + p2 = 0 + 15

Combine like terms: 0 + 15 = 15
-14.5p + p2 = 15

The p term is -14.5p.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5p + 52.5625 + p2 = 15 + 52.5625

Reorder the terms:
52.5625 + -14.5p + p2 = 15 + 52.5625

Combine like terms: 15 + 52.5625 = 67.5625
52.5625 + -14.5p + p2 = 67.5625

Factor a perfect square on the left side:
(p + -7.25)(p + -7.25) = 67.5625

Calculate the square root of the right side: 8.219641111

Break this problem into two subproblems by setting 
(p + -7.25) equal to 8.219641111 and -8.219641111.

Subproblem 1
p + -7.25 = 8.219641111

Simplifying
p + -7.25 = 8.219641111

Reorder the terms:
-7.25 + p = 8.219641111

Solving
-7.25 + p = 8.219641111

Solving for variable 'p'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + p = 8.219641111 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + p = 8.219641111 + 7.25
p = 8.219641111 + 7.25

Combine like terms: 8.219641111 + 7.25 = 15.469641111
p = 15.469641111

Simplifying
p = 15.469641111

Subproblem 2
p + -7.25 = -8.219641111

Simplifying
p + -7.25 = -8.219641111

Reorder the terms:
-7.25 + p = -8.219641111

Solving
-7.25 + p = -8.219641111

Solving for variable 'p'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + p = -8.219641111 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + p = -8.219641111 + 7.25
p = -8.219641111 + 7.25

Combine like terms: -8.219641111 + 7.25 = -0.969641111
p = -0.969641111

Simplifying
p = -0.969641111

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {15.469641111, -0.969641111}
Solution
p = {15.469641111, -0.969641111}