(4p-10)(p+3)=0

Solution for (4p-10)(p+3)=0 equation:

Simplifying
(4p + -10)(p + 3) = 0

Reorder the terms:
(-10 + 4p)(p + 3) = 0

Reorder the terms:
(-10 + 4p)(3 + p) = 0

Multiply (-10 + 4p) * (3 + p)
(-10(3 + p) + 4p * (3 + p)) = 0
((3 * -10 + p * -10) + 4p * (3 + p)) = 0
((-30 + -10p) + 4p * (3 + p)) = 0
(-30 + -10p + (3 * 4p + p * 4p)) = 0
(-30 + -10p + (12p + 4p2)) = 0

Combine like terms: -10p + 12p = 2p
(-30 + 2p + 4p2) = 0

Solving
-30 + 2p + 4p2 = 0

Solving for variable 'p'.

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

Factor a trinomial.
2((-3 + -1p)(5 + -2p)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-3, 2.5}