(2p+7)(3p-9)=

Solution for (2p+7)(3p-9)= equation:

Simplifying
(2p + 7)(3p + -9) = 0

Reorder the terms:
(7 + 2p)(3p + -9) = 0

Reorder the terms:
(7 + 2p)(-9 + 3p) = 0

Multiply (7 + 2p) * (-9 + 3p)
(7(-9 + 3p) + 2p * (-9 + 3p)) = 0
((-9 * 7 + 3p * 7) + 2p * (-9 + 3p)) = 0
((-63 + 21p) + 2p * (-9 + 3p)) = 0
(-63 + 21p + (-9 * 2p + 3p * 2p)) = 0
(-63 + 21p + (-18p + 6p2)) = 0

Combine like terms: 21p + -18p = 3p
(-63 + 3p + 6p2) = 0

Solving
-63 + 3p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + p + 2p2) = 0

Factor a trinomial.
3((-7 + -2p)(3 + -1p)) = 0

Ignore the factor 3.
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 + -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 = {-3.5, 3}