7p^2+1=5+12p

Solution for 7p^2+1=5+12p equation:

Simplifying
7p2 + 1 = 5 + 12p

Reorder the terms:
1 + 7p2 = 5 + 12p

Solving
1 + 7p2 = 5 + 12p

Solving for variable 'p'.

Reorder the terms:
1 + -5 + -12p + 7p2 = 5 + 12p + -5 + -12p

Combine like terms: 1 + -5 = -4
-4 + -12p + 7p2 = 5 + 12p + -5 + -12p

Reorder the terms:
-4 + -12p + 7p2 = 5 + -5 + 12p + -12p

Combine like terms: 5 + -5 = 0
-4 + -12p + 7p2 = 0 + 12p + -12p
-4 + -12p + 7p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
-4 + -12p + 7p2 = 0

Factor a trinomial.
(-2 + -7p)(2 + -1p) = 0

Subproblem 1
Set the factor '(-2 + -7p)' equal to zero and attempt to solve:

Simplifying
-2 + -7p = 0

Solving
-2 + -7p = 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 + -7p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7p = 0 + 2
-7p = 0 + 2

Combine like terms: 0 + 2 = 2
-7p = 2

Divide each side by '-7'.
p = -0.2857142857

Simplifying
p = -0.2857142857
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 = {-0.2857142857, 2}