(4r-3s)(2r+6s)=

Solution for (4r-3s)(2r+6s)= equation:

Simplifying
(4r + -3s)(2r + 6s) = 0

Multiply (4r + -3s) * (2r + 6s)
(4r * (2r + 6s) + -3s * (2r + 6s)) = 0
((2r * 4r + 6s * 4r) + -3s * (2r + 6s)) = 0

Reorder the terms:
((24rs + 8r2) + -3s * (2r + 6s)) = 0
((24rs + 8r2) + -3s * (2r + 6s)) = 0
(24rs + 8r2 + (2r * -3s + 6s * -3s)) = 0
(24rs + 8r2 + (-6rs + -18s2)) = 0

Reorder the terms:
(24rs + -6rs + 8r2 + -18s2) = 0

Combine like terms: 24rs + -6rs = 18rs
(18rs + 8r2 + -18s2) = 0

Solving
18rs + 8r2 + -18s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9rs + 4r2 + -9s2) = 0

Factor a trinomial.
2((4r + -3s)(r + 3s)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4r + -3s)' equal to zero and attempt to solve:

Simplifying
4r + -3s = 0

Solving
4r + -3s = 0

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

Add '3s' to each side of the equation.
4r + -3s + 3s = 0 + 3s

Combine like terms: -3s + 3s = 0
4r + 0 = 0 + 3s
4r = 0 + 3s
Remove the zero:
4r = 3s

Divide each side by '4'.
r = 0.75s

Simplifying
r = 0.75s
Subproblem 2
Set the factor '(r + 3s)' equal to zero and attempt to solve:

Simplifying
r + 3s = 0

Solving
r + 3s = 0

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

Add '-3s' to each side of the equation.
r + 3s + -3s = 0 + -3s

Combine like terms: 3s + -3s = 0
r + 0 = 0 + -3s
r = 0 + -3s
Remove the zero:
r = -3s

Simplifying
r = -3s
Solution
r = {0.75s, -3s}