(2r^2+7s^2)(2r^2-7s^2)=0

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Solution for (2r^2+7s^2)(2r^2-7s^2)=0 equation: 


Simplifying
(2r2 + 7s2)(2r2 + -7s2) = 0

Multiply (2r2 + 7s2) * (2r2 + -7s2)
(2r2 * (2r2 + -7s2) + 7s2 * (2r2 + -7s2)) = 0
((2r2 * 2r2 + -7s2 * 2r2) + 7s2 * (2r2 + -7s2)) = 0

Reorder the terms:
((-14r2s2 + 4r4) + 7s2 * (2r2 + -7s2)) = 0
((-14r2s2 + 4r4) + 7s2 * (2r2 + -7s2)) = 0
(-14r2s2 + 4r4 + (2r2 * 7s2 + -7s2 * 7s2)) = 0
(-14r2s2 + 4r4 + (14r2s2 + -49s4)) = 0

Reorder the terms:
(-14r2s2 + 14r2s2 + 4r4 + -49s4) = 0

Combine like terms: -14r2s2 + 14r2s2 = 0
(0 + 4r4 + -49s4) = 0
(4r4 + -49s4) = 0

Solving
4r4 + -49s4 = 0

Solving for variable 'r'.

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

Add '49s4' to each side of the equation.
4r4 + -49s4 + 49s4 = 0 + 49s4

Combine like terms: -49s4 + 49s4 = 0
4r4 + 0 = 0 + 49s4
4r4 = 0 + 49s4
Remove the zero:
4r4 = 49s4

Divide each side by '4'.
r4 = 12.25s4

Simplifying
r4 = 12.25s4

Combine like terms: 12.25s4 + -12.25s4 = 0.00
r4 + -12.25s4 = 0.00

Factor a difference between two squares.
(r2 + 3.5s2)(r2 + -3.5s2) = 0.00


Subproblem 1
Set the factor '(r2 + 3.5s2)' equal to zero and attempt to solve:

Simplifying
r2 + 3.5s2 = 0

Solving
r2 + 3.5s2 = 0

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

Add '-3.5s2' to each side of the equation.
r2 + 3.5s2 + -3.5s2 = 0 + -3.5s2

Combine like terms: 3.5s2 + -3.5s2 = 0.0
r2 + 0.0 = 0 + -3.5s2
r2 = 0 + -3.5s2
Remove the zero:
r2 = -3.5s2

Simplifying
r2 = -3.5s2

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 '(r2 + -3.5s2)' equal to zero and attempt to solve:

Simplifying
r2 + -3.5s2 = 0

Solving
r2 + -3.5s2 = 0

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

Add '3.5s2' to each side of the equation.
r2 + -3.5s2 + 3.5s2 = 0 + 3.5s2

Combine like terms: -3.5s2 + 3.5s2 = 0.0
r2 + 0.0 = 0 + 3.5s2
r2 = 0 + 3.5s2
Remove the zero:
r2 = 3.5s2

Simplifying
r2 = 3.5s2

Take the square root of each side:
r = {-1.870828693s, 1.870828693s}
Solution
r = {-1.870828693s, 1.870828693s}

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