6p^2=19p-3

Solution for 6p^2=19p-3 equation:

Simplifying
6p2 = 19p + -3

Reorder the terms:
6p2 = -3 + 19p

Solving
6p2 = -3 + 19p

Solving for variable 'p'.

Reorder the terms:
3 + -19p + 6p2 = -3 + 19p + 3 + -19p

Reorder the terms:
3 + -19p + 6p2 = -3 + 3 + 19p + -19p

Combine like terms: -3 + 3 = 0
3 + -19p + 6p2 = 0 + 19p + -19p
3 + -19p + 6p2 = 19p + -19p

Combine like terms: 19p + -19p = 0
3 + -19p + 6p2 = 0

Factor a trinomial.
(1 + -6p)(3 + -1p) = 0

Subproblem 1
Set the factor '(1 + -6p)' equal to zero and attempt to solve:

Simplifying
1 + -6p = 0

Solving
1 + -6p = 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 + -6p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6p = 0 + -1
-6p = 0 + -1

Combine like terms: 0 + -1 = -1
-6p = -1

Divide each side by '-6'.
p = 0.1666666667

Simplifying
p = 0.1666666667
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 = {0.1666666667, 3}