(5p^2-3)+(2p^2-3p^2)=0

Solution for (5p^2-3)+(2p^2-3p^2)=0 equation:

Simplifying
(5p2 + -3) + (2p2 + -3p2) = 0

Reorder the terms:
(-3 + 5p2) + (2p2 + -3p2) = 0

Remove parenthesis around (-3 + 5p2)
-3 + 5p2 + (2p2 + -3p2) = 0

Combine like terms: 2p2 + -3p2 = -1p2
-3 + 5p2 + (-1p2) = 0
-3 + 5p2 + (-1p2) = 0

Combine like terms: 5p2 + (-1p2) = 4p2
-3 + 4p2 = 0

Solving
-3 + 4p2 = 0

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + 4p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4p2 = 0 + 3
4p2 = 0 + 3

Combine like terms: 0 + 3 = 3
4p2 = 3

Divide each side by '4'.
p2 = 0.75

Simplifying
p2 = 0.75

Take the square root of each side:
p = {-0.866025404, 0.866025404}