12(p^2+1)=25p

Solution for 12(p^2+1)=25p equation:

Simplifying
12(p2 + 1) = 25p

Reorder the terms:
12(1 + p2) = 25p
(1 * 12 + p2 * 12) = 25p
(12 + 12p2) = 25p

Solving
12 + 12p2 = 25p

Solving for variable 'p'.

Reorder the terms:
12 + -25p + 12p2 = 25p + -25p

Combine like terms: 25p + -25p = 0
12 + -25p + 12p2 = 0

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

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

Simplifying
3 + -4p = 0

Solving
3 + -4p = 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 + -4p = 0 + -3

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

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

Divide each side by '-4'.
p = 0.75

Simplifying
p = 0.75
Subproblem 2
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
Solution
p = {0.75, 1.333333333}