12p^2-38p+37=2p+5

Solution for 12p^2-38p+37=2p+5 equation:

Simplifying
12p2 + -38p + 37 = 2p + 5

Reorder the terms:
37 + -38p + 12p2 = 2p + 5

Reorder the terms:
37 + -38p + 12p2 = 5 + 2p

Solving
37 + -38p + 12p2 = 5 + 2p

Solving for variable 'p'.

Reorder the terms:
37 + -5 + -38p + -2p + 12p2 = 5 + 2p + -5 + -2p

Combine like terms: 37 + -5 = 32
32 + -38p + -2p + 12p2 = 5 + 2p + -5 + -2p

Combine like terms: -38p + -2p = -40p
32 + -40p + 12p2 = 5 + 2p + -5 + -2p

Reorder the terms:
32 + -40p + 12p2 = 5 + -5 + 2p + -2p

Combine like terms: 5 + -5 = 0
32 + -40p + 12p2 = 0 + 2p + -2p
32 + -40p + 12p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
32 + -40p + 12p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -10p + 3p2) = 0

Factor a trinomial.
4((4 + -3p)(2 + -1p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(4 + -3p)' equal to zero and attempt to solve:

Simplifying
4 + -3p = 0

Solving
4 + -3p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3p = 0 + -4
-3p = 0 + -4

Combine like terms: 0 + -4 = -4
-3p = -4

Divide each side by '-3'.
p = 1.333333333

Simplifying
p = 1.333333333
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 = {1.333333333, 2}