(3p+4)(p+3)=(8p+9)(p)

Solution for (3p+4)(p+3)=(8p+9)(p) equation:

Simplifying
(3p + 4)(p + 3) = (8p + 9)(p)

Reorder the terms:
(4 + 3p)(p + 3) = (8p + 9)(p)

Reorder the terms:
(4 + 3p)(3 + p) = (8p + 9)(p)

Multiply (4 + 3p) * (3 + p)
(4(3 + p) + 3p * (3 + p)) = (8p + 9)(p)
((3 * 4 + p * 4) + 3p * (3 + p)) = (8p + 9)(p)
((12 + 4p) + 3p * (3 + p)) = (8p + 9)(p)
(12 + 4p + (3 * 3p + p * 3p)) = (8p + 9)(p)
(12 + 4p + (9p + 3p2)) = (8p + 9)(p)

Combine like terms: 4p + 9p = 13p
(12 + 13p + 3p2) = (8p + 9)(p)

Reorder the terms:
12 + 13p + 3p2 = (9 + 8p)(p)

Reorder the terms for easier multiplication:
12 + 13p + 3p2 = p(9 + 8p)
12 + 13p + 3p2 = (9 * p + 8p * p)
12 + 13p + 3p2 = (9p + 8p2)

Solving
12 + 13p + 3p2 = 9p + 8p2

Solving for variable 'p'.

Reorder the terms:
12 + 13p + -9p + 3p2 + -8p2 = 9p + 8p2 + -9p + -8p2

Combine like terms: 13p + -9p = 4p
12 + 4p + 3p2 + -8p2 = 9p + 8p2 + -9p + -8p2

Combine like terms: 3p2 + -8p2 = -5p2
12 + 4p + -5p2 = 9p + 8p2 + -9p + -8p2

Reorder the terms:
12 + 4p + -5p2 = 9p + -9p + 8p2 + -8p2

Combine like terms: 9p + -9p = 0
12 + 4p + -5p2 = 0 + 8p2 + -8p2
12 + 4p + -5p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
12 + 4p + -5p2 = 0

Factor a trinomial.
(2 + -1p)(6 + 5p) = 0

Subproblem 1
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Subproblem 2
Set the factor '(6 + 5p)' equal to zero and attempt to solve:

Simplifying
6 + 5p = 0

Solving
6 + 5p = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5p = 0 + -6
5p = 0 + -6

Combine like terms: 0 + -6 = -6
5p = -6

Divide each side by '5'.
p = -1.2

Simplifying
p = -1.2
Solution
p = {2, -1.2}