3(p-3)5p=-3p-6

Solution for 3(p-3)5p=-3p-6 equation:

Simplifying
3(p + -3) * 5p = -3p + -6

Reorder the terms:
3(-3 + p) * 5p = -3p + -6

Reorder the terms for easier multiplication:
3 * 5p(-3 + p) = -3p + -6

Multiply 3 * 5
15p(-3 + p) = -3p + -6
(-3 * 15p + p * 15p) = -3p + -6
(-45p + 15p2) = -3p + -6

Reorder the terms:
-45p + 15p2 = -6 + -3p

Solving
-45p + 15p2 = -6 + -3p

Solving for variable 'p'.

Reorder the terms:
6 + -45p + 3p + 15p2 = -6 + -3p + 6 + 3p

Combine like terms: -45p + 3p = -42p
6 + -42p + 15p2 = -6 + -3p + 6 + 3p

Reorder the terms:
6 + -42p + 15p2 = -6 + 6 + -3p + 3p

Combine like terms: -6 + 6 = 0
6 + -42p + 15p2 = 0 + -3p + 3p
6 + -42p + 15p2 = -3p + 3p

Combine like terms: -3p + 3p = 0
6 + -42p + 15p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -14p + 5p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -14p + 5p2)' equal to zero and attempt to solve:

Simplifying
2 + -14p + 5p2 = 0

Solving
2 + -14p + 5p2 = 0

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

Divide each side by '5'.
0.4 + -2.8p + p2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.8p + -0.4 + p2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.8p + p2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.8p + p2 = 0 + -0.4
-2.8p + p2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.8p + p2 = -0.4

The p term is -2.8p.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8p + 1.96 + p2 = -0.4 + 1.96

Reorder the terms:
1.96 + -2.8p + p2 = -0.4 + 1.96

Combine like terms: -0.4 + 1.96 = 1.56
1.96 + -2.8p + p2 = 1.56

Factor a perfect square on the left side:
(p + -1.4)(p + -1.4) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(p + -1.4) equal to 1.2489996 and -1.2489996.

Subproblem 1
p + -1.4 = 1.2489996

Simplifying
p + -1.4 = 1.2489996

Reorder the terms:
-1.4 + p = 1.2489996

Solving
-1.4 + p = 1.2489996

Solving for variable 'p'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + p = 1.2489996 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + p = 1.2489996 + 1.4
p = 1.2489996 + 1.4

Combine like terms: 1.2489996 + 1.4 = 2.6489996
p = 2.6489996

Simplifying
p = 2.6489996

Subproblem 2
p + -1.4 = -1.2489996

Simplifying
p + -1.4 = -1.2489996

Reorder the terms:
-1.4 + p = -1.2489996

Solving
-1.4 + p = -1.2489996

Solving for variable 'p'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + p = -1.2489996 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + p = -1.2489996 + 1.4
p = -1.2489996 + 1.4

Combine like terms: -1.2489996 + 1.4 = 0.1510004
p = 0.1510004

Simplifying
p = 0.1510004

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.6489996, 0.1510004}
Solution
p = {2.6489996, 0.1510004}