(2p+3)(2p-4)=8

Solution for (2p+3)(2p-4)=8 equation:

Simplifying
(2p + 3)(2p + -4) = 8

Reorder the terms:
(3 + 2p)(2p + -4) = 8

Reorder the terms:
(3 + 2p)(-4 + 2p) = 8

Multiply (3 + 2p) * (-4 + 2p)
(3(-4 + 2p) + 2p * (-4 + 2p)) = 8
((-4 * 3 + 2p * 3) + 2p * (-4 + 2p)) = 8
((-12 + 6p) + 2p * (-4 + 2p)) = 8
(-12 + 6p + (-4 * 2p + 2p * 2p)) = 8
(-12 + 6p + (-8p + 4p2)) = 8

Combine like terms: 6p + -8p = -2p
(-12 + -2p + 4p2) = 8

Solving
-12 + -2p + 4p2 = 8

Solving for variable 'p'.

Reorder the terms:
-12 + -8 + -2p + 4p2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + -2p + 4p2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + -2p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1p + 2p2) = 0

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

Ignore the factor 2.
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 '(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 = {-2, 2.5}