2p^2=5p+3

Solution for 2p^2=5p+3 equation:

Simplifying
2p2 = 5p + 3

Reorder the terms:
2p2 = 3 + 5p

Solving
2p2 = 3 + 5p

Solving for variable 'p'.

Reorder the terms:
-3 + -5p + 2p2 = 3 + 5p + -3 + -5p

Reorder the terms:
-3 + -5p + 2p2 = 3 + -3 + 5p + -5p

Combine like terms: 3 + -3 = 0
-3 + -5p + 2p2 = 0 + 5p + -5p
-3 + -5p + 2p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
-3 + -5p + 2p2 = 0

Factor a trinomial.
(-1 + -2p)(3 + -1p) = 0

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

Simplifying
-1 + -2p = 0

Solving
-1 + -2p = 0

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

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

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

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

Divide each side by '-2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-0.5, 3}