6p^2+9p-45=0

Solution for 6p^2+9p-45=0 equation:

Simplifying
6p2 + 9p + -45 = 0

Reorder the terms:
-45 + 9p + 6p2 = 0

Solving
-45 + 9p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 3p + 2p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-15 + 3p + 2p2)' equal to zero and attempt to solve:

Simplifying
-15 + 3p + 2p2 = 0

Solving
-15 + 3p + 2p2 = 0

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

Divide each side by '2'.
-7.5 + 1.5p + p2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 1.5p + 7.5 + p2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 1.5p + p2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 1.5p + p2 = 0 + 7.5
1.5p + p2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
1.5p + p2 = 7.5

The p term is 1.5p.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5p + 0.5625 + p2 = 7.5 + 0.5625

Reorder the terms:
0.5625 + 1.5p + p2 = 7.5 + 0.5625

Combine like terms: 7.5 + 0.5625 = 8.0625
0.5625 + 1.5p + p2 = 8.0625

Factor a perfect square on the left side:
(p + 0.75)(p + 0.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(p + 0.75) equal to 2.839454173 and -2.839454173.

Subproblem 1
p + 0.75 = 2.839454173

Simplifying
p + 0.75 = 2.839454173

Reorder the terms:
0.75 + p = 2.839454173

Solving
0.75 + p = 2.839454173

Solving for variable 'p'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + p = 2.839454173 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + p = 2.839454173 + -0.75
p = 2.839454173 + -0.75

Combine like terms: 2.839454173 + -0.75 = 2.089454173
p = 2.089454173

Simplifying
p = 2.089454173

Subproblem 2
p + 0.75 = -2.839454173

Simplifying
p + 0.75 = -2.839454173

Reorder the terms:
0.75 + p = -2.839454173

Solving
0.75 + p = -2.839454173

Solving for variable 'p'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + p = -2.839454173 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + p = -2.839454173 + -0.75
p = -2.839454173 + -0.75

Combine like terms: -2.839454173 + -0.75 = -3.589454173
p = -3.589454173

Simplifying
p = -3.589454173

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.089454173, -3.589454173}
Solution
p = {2.089454173, -3.589454173}