7p^2-49p=56

Solution for 7p^2-49p=56 equation:

Simplifying
7p2 + -49p = 56

Reorder the terms:
-49p + 7p2 = 56

Solving
-49p + 7p2 = 56

Solving for variable 'p'.

Reorder the terms:
-56 + -49p + 7p2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -49p + 7p2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -7p + p2) = 0

Factor a trinomial.
7((-1 + -1p)(8 + -1p)) = 0

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1p = 0 + -8
-1p = 0 + -8

Combine like terms: 0 + -8 = -8
-1p = -8

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {-1, 8}