(2p-3)(2p+7)=0

Solution for (2p-3)(2p+7)=0 equation:

Simplifying
(2p + -3)(2p + 7) = 0

Reorder the terms:
(-3 + 2p)(2p + 7) = 0

Reorder the terms:
(-3 + 2p)(7 + 2p) = 0

Multiply (-3 + 2p) * (7 + 2p)
(-3(7 + 2p) + 2p * (7 + 2p)) = 0
((7 * -3 + 2p * -3) + 2p * (7 + 2p)) = 0
((-21 + -6p) + 2p * (7 + 2p)) = 0
(-21 + -6p + (7 * 2p + 2p * 2p)) = 0
(-21 + -6p + (14p + 4p2)) = 0

Combine like terms: -6p + 14p = 8p
(-21 + 8p + 4p2) = 0

Solving
-21 + 8p + 4p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-7 + -2p)(3 + -2p) = 0

Subproblem 1
Set the factor '(-7 + -2p)' equal to zero and attempt to solve:

Simplifying
-7 + -2p = 0

Solving
-7 + -2p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2p = 0 + 7
-2p = 0 + 7

Combine like terms: 0 + 7 = 7
-2p = 7

Divide each side by '-2'.
p = -3.5

Simplifying
p = -3.5
Subproblem 2
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
Solution
p = {-3.5, 1.5}