8p^4q^4-11p^2q^2+3=

Solution for 8p^4q^4-11p^2q^2+3= equation:

Simplifying
8p4q4 + -11p2q2 + 3 = 0

Reorder the terms:
3 + -11p2q2 + 8p4q4 = 0

Solving
3 + -11p2q2 + 8p4q4 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + -8p2q2)(1 + -1p2q2) = 0

Factor a difference between two squares.
(3 + -8p2q2)((1 + pq)(1 + -1pq)) = 0

Subproblem 1
Set the factor '(3 + -8p2q2)' equal to zero and attempt to solve:

Simplifying
3 + -8p2q2 = 0

Solving
3 + -8p2q2 = 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 + -8p2q2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8p2q2 = 0 + -3
-8p2q2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8p2q2 = -3

Divide each side by '-8q2'.
p2 = 0.375q-2

Simplifying
p2 = 0.375q-2

Take the square root of each side:
p = {-0.612372436q-1, 0.612372436q-1}
Subproblem 2
Set the factor '(1 + pq)' equal to zero and attempt to solve:

Simplifying
1 + pq = 0

Solving
1 + pq = 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 + pq = 0 + -1

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

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

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

Simplifying
p = -1q-1
Subproblem 3
Set the factor '(1 + -1pq)' equal to zero and attempt to solve:

Simplifying
1 + -1pq = 0

Solving
1 + -1pq = 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 + -1pq = 0 + -1

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

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

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

Simplifying
p = q-1
Solution
p = {-0.612372436q-1, 0.612372436q-1, -1q-1, q-1}