2+9p-2p^2=4(p+1)

Solution for 2+9p-2p^2=4(p+1) equation:

Simplifying
2 + 9p + -2p2 = 4(p + 1)

Reorder the terms:
2 + 9p + -2p2 = 4(1 + p)
2 + 9p + -2p2 = (1 * 4 + p * 4)
2 + 9p + -2p2 = (4 + 4p)

Solving
2 + 9p + -2p2 = 4 + 4p

Solving for variable 'p'.

Reorder the terms:
2 + -4 + 9p + -4p + -2p2 = 4 + 4p + -4 + -4p

Combine like terms: 2 + -4 = -2
-2 + 9p + -4p + -2p2 = 4 + 4p + -4 + -4p

Combine like terms: 9p + -4p = 5p
-2 + 5p + -2p2 = 4 + 4p + -4 + -4p

Reorder the terms:
-2 + 5p + -2p2 = 4 + -4 + 4p + -4p

Combine like terms: 4 + -4 = 0
-2 + 5p + -2p2 = 0 + 4p + -4p
-2 + 5p + -2p2 = 4p + -4p

Combine like terms: 4p + -4p = 0
-2 + 5p + -2p2 = 0

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

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

Simplifying
-2 + p = 0

Solving
-2 + p = 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 + p = 0 + 2

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

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

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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {2, 0.5}