5p^2(p^2-4)=20-41p^2

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Solution for 5p^2(p^2-4)=20-41p^2 equation: 


Simplifying
5p2(p2 + -4) = 20 + -41p2

Reorder the terms:
5p2(-4 + p2) = 20 + -41p2
(-4 * 5p2 + p2 * 5p2) = 20 + -41p2
(-20p2 + 5p4) = 20 + -41p2

Solving
-20p2 + 5p4 = 20 + -41p2

Solving for variable 'p'.

Reorder the terms:
-20 + -20p2 + 41p2 + 5p4 = 20 + -41p2 + -20 + 41p2

Combine like terms: -20p2 + 41p2 = 21p2
-20 + 21p2 + 5p4 = 20 + -41p2 + -20 + 41p2

Reorder the terms:
-20 + 21p2 + 5p4 = 20 + -20 + -41p2 + 41p2

Combine like terms: 20 + -20 = 0
-20 + 21p2 + 5p4 = 0 + -41p2 + 41p2
-20 + 21p2 + 5p4 = -41p2 + 41p2

Combine like terms: -41p2 + 41p2 = 0
-20 + 21p2 + 5p4 = 0

Factor a trinomial.
(-5 + -1p2)(4 + -5p2) = 0


Subproblem 1
Set the factor '(-5 + -1p2)' equal to zero and attempt to solve:

Simplifying
-5 + -1p2 = 0

Solving
-5 + -1p2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p2 = 0 + 5
-1p2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1p2 = 5

Divide each side by '-1'.
p2 = -5

Simplifying
p2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4 + -5p2)' equal to zero and attempt to solve:

Simplifying
4 + -5p2 = 0

Solving
4 + -5p2 = 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 + -5p2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5p2 = 0 + -4
-5p2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5p2 = -4

Divide each side by '-5'.
p2 = 0.8

Simplifying
p2 = 0.8

Take the square root of each side:
p = {-0.894427191, 0.894427191}
Solution
p = {-0.894427191, 0.894427191}

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