(4p+5)(2p-9)=

Solution for (4p+5)(2p-9)= equation:

Simplifying
(4p + 5)(2p + -9) = 0

Reorder the terms:
(5 + 4p)(2p + -9) = 0

Reorder the terms:
(5 + 4p)(-9 + 2p) = 0

Multiply (5 + 4p) * (-9 + 2p)
(5(-9 + 2p) + 4p * (-9 + 2p)) = 0
((-9 * 5 + 2p * 5) + 4p * (-9 + 2p)) = 0
((-45 + 10p) + 4p * (-9 + 2p)) = 0
(-45 + 10p + (-9 * 4p + 2p * 4p)) = 0
(-45 + 10p + (-36p + 8p2)) = 0

Combine like terms: 10p + -36p = -26p
(-45 + -26p + 8p2) = 0

Solving
-45 + -26p + 8p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5 + -4p)(9 + -2p) = 0

Subproblem 1
Set the factor '(-5 + -4p)' equal to zero and attempt to solve:

Simplifying
-5 + -4p = 0

Solving
-5 + -4p = 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 + -4p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4p = 0 + 5
-4p = 0 + 5

Combine like terms: 0 + 5 = 5
-4p = 5

Divide each side by '-4'.
p = -1.25

Simplifying
p = -1.25
Subproblem 2
Set the factor '(9 + -2p)' equal to zero and attempt to solve:

Simplifying
9 + -2p = 0

Solving
9 + -2p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2p = 0 + -9
-2p = 0 + -9

Combine like terms: 0 + -9 = -9
-2p = -9

Divide each side by '-2'.
p = 4.5

Simplifying
p = 4.5
Solution
p = {-1.25, 4.5}