5p^2-16p+9=6

Solution for 5p^2-16p+9=6 equation:

Simplifying
5p2 + -16p + 9 = 6

Reorder the terms:
9 + -16p + 5p2 = 6

Solving
9 + -16p + 5p2 = 6

Solving for variable 'p'.

Reorder the terms:
9 + -6 + -16p + 5p2 = 6 + -6

Combine like terms: 9 + -6 = 3
3 + -16p + 5p2 = 6 + -6

Combine like terms: 6 + -6 = 0
3 + -16p + 5p2 = 0

Factor a trinomial.
(1 + -5p)(3 + -1p) = 0

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

Simplifying
1 + -5p = 0

Solving
1 + -5p = 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 + -5p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5p = 0 + -1
-5p = 0 + -1

Combine like terms: 0 + -1 = -1
-5p = -1

Divide each side by '-5'.
p = 0.2

Simplifying
p = 0.2
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 = {0.2, 3}