4p^2=-9p-2

Solution for 4p^2=-9p-2 equation:

Simplifying
4p2 = -9p + -2

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

Solving
4p2 = -2 + -9p

Solving for variable 'p'.

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

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

Combine like terms: -2 + 2 = 0
2 + 9p + 4p2 = 0 + -9p + 9p
2 + 9p + 4p2 = -9p + 9p

Combine like terms: -9p + 9p = 0
2 + 9p + 4p2 = 0

Factor a trinomial.
(2 + p)(1 + 4p) = 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 + 4p)' equal to zero and attempt to solve:

Simplifying
1 + 4p = 0

Solving
1 + 4p = 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 + 4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4p = 0 + -1
4p = 0 + -1

Combine like terms: 0 + -1 = -1
4p = -1

Divide each side by '4'.
p = -0.25

Simplifying
p = -0.25
Solution
p = {-2, -0.25}