4r^2+7r+3s^2=

Solution for 4r^2+7r+3s^2= equation:

Simplifying
4r2 + 7r + 3s2 = 0

Reorder the terms:
7r + 4r2 + 3s2 = 0

Solving
7r + 4r2 + 3s2 = 0

Solving for variable 'r'.

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

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 + s)' equal to zero and attempt to solve:

Simplifying
r + s = 0

Solving
r + s = 0

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

Add '-1s' to each side of the equation.
r + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
r + 0 = 0 + -1s
r = 0 + -1s
Remove the zero:
r = -1s

Simplifying
r = -1s
Solution
r = {-0.75s, -1s}