2p^2+8p=42

Solution for 2p^2+8p=42 equation:

Simplifying
2p2 + 8p = 42

Reorder the terms:
8p + 2p2 = 42

Solving
8p + 2p2 = 42

Solving for variable 'p'.

Reorder the terms:
-42 + 8p + 2p2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 8p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 4p + p2) = 0

Factor a trinomial.
2((-7 + -1p)(3 + -1p)) = 0

Ignore the factor 2.
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 '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-7, 3}