3p^2=-5p+112

Solution for 3p^2=-5p+112 equation:

Simplifying
3p2 = -5p + 112

Reorder the terms:
3p2 = 112 + -5p

Solving
3p2 = 112 + -5p

Solving for variable 'p'.

Reorder the terms:
-112 + 5p + 3p2 = 112 + -5p + -112 + 5p

Reorder the terms:
-112 + 5p + 3p2 = 112 + -112 + -5p + 5p

Combine like terms: 112 + -112 = 0
-112 + 5p + 3p2 = 0 + -5p + 5p
-112 + 5p + 3p2 = -5p + 5p

Combine like terms: -5p + 5p = 0
-112 + 5p + 3p2 = 0

Factor a trinomial.
(-7 + -1p)(16 + -3p) = 0

Subproblem 1
Set the factor '(-7 + -1p)' equal to zero and attempt to solve:

Simplifying
-7 + -1p = 0

Solving
-7 + -1p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1p = 0 + 7
-1p = 0 + 7

Combine like terms: 0 + 7 = 7
-1p = 7

Divide each side by '-1'.
p = -7

Simplifying
p = -7
Subproblem 2
Set the factor '(16 + -3p)' equal to zero and attempt to solve:

Simplifying
16 + -3p = 0

Solving
16 + -3p = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3p = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3p = 0 + -16
-3p = 0 + -16

Combine like terms: 0 + -16 = -16
-3p = -16

Divide each side by '-3'.
p = 5.333333333

Simplifying
p = 5.333333333
Solution
p = {-7, 5.333333333}