3p^2-30p+51=3

Solution for 3p^2-30p+51=3 equation:

Simplifying
3p2 + -30p + 51 = 3

Reorder the terms:
51 + -30p + 3p2 = 3

Solving
51 + -30p + 3p2 = 3

Solving for variable 'p'.

Reorder the terms:
51 + -3 + -30p + 3p2 = 3 + -3

Combine like terms: 51 + -3 = 48
48 + -30p + 3p2 = 3 + -3

Combine like terms: 3 + -3 = 0
48 + -30p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -10p + p2) = 0

Factor a trinomial.
3((2 + -1p)(8 + -1p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

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

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

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1p = 0 + -8
-1p = 0 + -8

Combine like terms: 0 + -8 = -8
-1p = -8

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {2, 8}