5p^2+42=-41p

Solution for 5p^2+42=-41p equation:

Simplifying
5p2 + 42 = -41p

Reorder the terms:
42 + 5p2 = -41p

Solving
42 + 5p2 = -41p

Solving for variable 'p'.

Reorder the terms:
42 + 41p + 5p2 = -41p + 41p

Combine like terms: -41p + 41p = 0
42 + 41p + 5p2 = 0

Factor a trinomial.
(7 + p)(6 + 5p) = 0

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

Simplifying
7 + p = 0

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

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

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

Simplifying
p = -7
Subproblem 2
Set the factor '(6 + 5p)' equal to zero and attempt to solve:

Simplifying
6 + 5p = 0

Solving
6 + 5p = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5p = 0 + -6
5p = 0 + -6

Combine like terms: 0 + -6 = -6
5p = -6

Divide each side by '5'.
p = -1.2

Simplifying
p = -1.2
Solution
p = {-7, -1.2}