4p^2-13p=-15+3p

Solution for 4p^2-13p=-15+3p equation:

Simplifying
4p2 + -13p = -15 + 3p

Reorder the terms:
-13p + 4p2 = -15 + 3p

Solving
-13p + 4p2 = -15 + 3p

Solving for variable 'p'.

Reorder the terms:
15 + -13p + -3p + 4p2 = -15 + 3p + 15 + -3p

Combine like terms: -13p + -3p = -16p
15 + -16p + 4p2 = -15 + 3p + 15 + -3p

Reorder the terms:
15 + -16p + 4p2 = -15 + 15 + 3p + -3p

Combine like terms: -15 + 15 = 0
15 + -16p + 4p2 = 0 + 3p + -3p
15 + -16p + 4p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
15 + -16p + 4p2 = 0

Factor a trinomial.
(3 + -2p)(5 + -2p) = 0

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

Simplifying
3 + -2p = 0

Solving
3 + -2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2p = 0 + -3
-2p = 0 + -3

Combine like terms: 0 + -3 = -3
-2p = -3

Divide each side by '-2'.
p = 1.5

Simplifying
p = 1.5
Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve:

Simplifying
5 + -2p = 0

Solving
5 + -2p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2p = 0 + -5
-2p = 0 + -5

Combine like terms: 0 + -5 = -5
-2p = -5

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Solution
p = {1.5, 2.5}