20p^3+70p^2-56p=-p^3

Solution for 20p^3+70p^2-56p=-p^3 equation:

Simplifying
20p3 + 70p2 + -56p = -1p3

Reorder the terms:
-56p + 70p2 + 20p3 = -1p3

Solving
-56p + 70p2 + 20p3 = -1p3

Solving for variable 'p'.

Combine like terms: 20p3 + p3 = 21p3
-56p + 70p2 + 21p3 = -1p3 + p3

Combine like terms: -1p3 + p3 = 0
-56p + 70p2 + 21p3 = 0

Factor out the Greatest Common Factor (GCF), '7p'.
7p(-8 + 10p + 3p2) = 0

Factor a trinomial.
7p((-4 + -1p)(2 + -3p)) = 0

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4
Subproblem 3
Set the factor '(2 + -3p)' equal to zero and attempt to solve:

Simplifying
2 + -3p = 0

Solving
2 + -3p = 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 + -3p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3p = 0 + -2
-3p = 0 + -2

Combine like terms: 0 + -2 = -2
-3p = -2

Divide each side by '-3'.
p = 0.6666666667

Simplifying
p = 0.6666666667
Solution
p = {0, -4, 0.6666666667}