(5r+3f)(5r-3f)=

Solution for (5r+3f)(5r-3f)= equation:

Simplifying
(5r + 3f)(5r + -3f) = 0

Reorder the terms:
(3f + 5r)(5r + -3f) = 0

Reorder the terms:
(3f + 5r)(-3f + 5r) = 0

Multiply (3f + 5r) * (-3f + 5r)
(3f * (-3f + 5r) + 5r * (-3f + 5r)) = 0
((-3f * 3f + 5r * 3f) + 5r * (-3f + 5r)) = 0

Reorder the terms:
((15fr + -9f2) + 5r * (-3f + 5r)) = 0
((15fr + -9f2) + 5r * (-3f + 5r)) = 0
(15fr + -9f2 + (-3f * 5r + 5r * 5r)) = 0
(15fr + -9f2 + (-15fr + 25r2)) = 0

Reorder the terms:
(15fr + -15fr + -9f2 + 25r2) = 0

Combine like terms: 15fr + -15fr = 0
(0 + -9f2 + 25r2) = 0
(-9f2 + 25r2) = 0

Solving
-9f2 + 25r2 = 0

Solving for variable 'f'.

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

Add '-25r2' to each side of the equation.
-9f2 + 25r2 + -25r2 = 0 + -25r2

Combine like terms: 25r2 + -25r2 = 0
-9f2 + 0 = 0 + -25r2
-9f2 = 0 + -25r2
Remove the zero:
-9f2 = -25r2

Divide each side by '-9'.
f2 = 2.777777778r2

Simplifying
f2 = 2.777777778r2

Take the square root of each side:
f = {-1.666666667r, 1.666666667r}