2p^2+3p=77

Solution for 2p^2+3p=77 equation:

Simplifying
2p2 + 3p = 77

Reorder the terms:
3p + 2p2 = 77

Solving
3p + 2p2 = 77

Solving for variable 'p'.

Reorder the terms:
-77 + 3p + 2p2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 3p + 2p2 = 0

Factor a trinomial.
(-7 + -1p)(11 + -2p) = 0

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

Simplifying
-7 + -1p = 0

Solving
-7 + -1p = 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 + -1p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1p = 0 + 7
-1p = 0 + 7

Combine like terms: 0 + 7 = 7
-1p = 7

Divide each side by '-1'.
p = -7

Simplifying
p = -7
Subproblem 2
Set the factor '(11 + -2p)' equal to zero and attempt to solve:

Simplifying
11 + -2p = 0

Solving
11 + -2p = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2p = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2p = 0 + -11
-2p = 0 + -11

Combine like terms: 0 + -11 = -11
-2p = -11

Divide each side by '-2'.
p = 5.5

Simplifying
p = 5.5
Solution
p = {-7, 5.5}