6p^2-21p+9=0

Solution for 6p^2-21p+9=0 equation:

Simplifying
6p2 + -21p + 9 = 0

Reorder the terms:
9 + -21p + 6p2 = 0

Solving
9 + -21p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -7p + 2p2) = 0

Factor a trinomial.
3((1 + -2p)(3 + -1p)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {0.5, 3}