-4p^2-21p+17=-7p^2-1

Solution for -4p^2-21p+17=-7p^2-1 equation:

Simplifying
-4p2 + -21p + 17 = -7p2 + -1

Reorder the terms:
17 + -21p + -4p2 = -7p2 + -1

Reorder the terms:
17 + -21p + -4p2 = -1 + -7p2

Solving
17 + -21p + -4p2 = -1 + -7p2

Solving for variable 'p'.

Reorder the terms:
17 + 1 + -21p + -4p2 + 7p2 = -1 + -7p2 + 1 + 7p2

Combine like terms: 17 + 1 = 18
18 + -21p + -4p2 + 7p2 = -1 + -7p2 + 1 + 7p2

Combine like terms: -4p2 + 7p2 = 3p2
18 + -21p + 3p2 = -1 + -7p2 + 1 + 7p2

Reorder the terms:
18 + -21p + 3p2 = -1 + 1 + -7p2 + 7p2

Combine like terms: -1 + 1 = 0
18 + -21p + 3p2 = 0 + -7p2 + 7p2
18 + -21p + 3p2 = -7p2 + 7p2

Combine like terms: -7p2 + 7p2 = 0
18 + -21p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7p + p2) = 0

Factor a trinomial.
3((1 + -1p)(6 + -1p)) = 0

Ignore the factor 3.
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 '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 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 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {1, 6}