6p^2-13p+6=3p-2

Solution for 6p^2-13p+6=3p-2 equation:

Simplifying
6p2 + -13p + 6 = 3p + -2

Reorder the terms:
6 + -13p + 6p2 = 3p + -2

Reorder the terms:
6 + -13p + 6p2 = -2 + 3p

Solving
6 + -13p + 6p2 = -2 + 3p

Solving for variable 'p'.

Reorder the terms:
6 + 2 + -13p + -3p + 6p2 = -2 + 3p + 2 + -3p

Combine like terms: 6 + 2 = 8
8 + -13p + -3p + 6p2 = -2 + 3p + 2 + -3p

Combine like terms: -13p + -3p = -16p
8 + -16p + 6p2 = -2 + 3p + 2 + -3p

Reorder the terms:
8 + -16p + 6p2 = -2 + 2 + 3p + -3p

Combine like terms: -2 + 2 = 0
8 + -16p + 6p2 = 0 + 3p + -3p
8 + -16p + 6p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
8 + -16p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -8p + 3p2) = 0

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

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

Simplifying
2 + -3p = 0

Solving
2 + -3p = 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 + -3p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3p = 0 + -2
-3p = 0 + -2

Combine like terms: 0 + -2 = -2
-3p = -2

Divide each side by '-3'.
p = 0.6666666667

Simplifying
p = 0.6666666667
Subproblem 2
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
Solution
p = {0.6666666667, 2}