(5r+7s)(5r-7s)=

Solution for (5r+7s)(5r-7s)= equation:

Simplifying
(5r + 7s)(5r + -7s) = 0

Multiply (5r + 7s) * (5r + -7s)
(5r * (5r + -7s) + 7s * (5r + -7s)) = 0
((5r * 5r + -7s * 5r) + 7s * (5r + -7s)) = 0

Reorder the terms:
((-35rs + 25r2) + 7s * (5r + -7s)) = 0
((-35rs + 25r2) + 7s * (5r + -7s)) = 0
(-35rs + 25r2 + (5r * 7s + -7s * 7s)) = 0
(-35rs + 25r2 + (35rs + -49s2)) = 0

Reorder the terms:
(-35rs + 35rs + 25r2 + -49s2) = 0

Combine like terms: -35rs + 35rs = 0
(0 + 25r2 + -49s2) = 0
(25r2 + -49s2) = 0

Solving
25r2 + -49s2 = 0

Solving for variable 'r'.

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

Add '49s2' to each side of the equation.
25r2 + -49s2 + 49s2 = 0 + 49s2

Combine like terms: -49s2 + 49s2 = 0
25r2 + 0 = 0 + 49s2
25r2 = 0 + 49s2
Remove the zero:
25r2 = 49s2

Divide each side by '25'.
r2 = 1.96s2

Simplifying
r2 = 1.96s2

Take the square root of each side:
r = {-1.4s, 1.4s}