4p^2-13p+12=3p

Solution for 4p^2-13p+12=3p equation:

Simplifying
4p2 + -13p + 12 = 3p

Reorder the terms:
12 + -13p + 4p2 = 3p

Solving
12 + -13p + 4p2 = 3p

Solving for variable 'p'.

Reorder the terms:
12 + -13p + -3p + 4p2 = 3p + -3p

Combine like terms: -13p + -3p = -16p
12 + -16p + 4p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
12 + -16p + 4p2 = 0

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

Factor a trinomial.
4((1 + -1p)(3 + -1p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

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

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

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

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

Simplifying
p = 1
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 = {1, 3}