(5r-7s)(4r+3s)=0

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Solution for (5r-7s)(4r+3s)=0 equation: 


Simplifying
(5r + -7s)(4r + 3s) = 0

Multiply (5r + -7s) * (4r + 3s)
(5r * (4r + 3s) + -7s * (4r + 3s)) = 0
((4r * 5r + 3s * 5r) + -7s * (4r + 3s)) = 0

Reorder the terms:
((15rs + 20r2) + -7s * (4r + 3s)) = 0
((15rs + 20r2) + -7s * (4r + 3s)) = 0
(15rs + 20r2 + (4r * -7s + 3s * -7s)) = 0
(15rs + 20r2 + (-28rs + -21s2)) = 0

Reorder the terms:
(15rs + -28rs + 20r2 + -21s2) = 0

Combine like terms: 15rs + -28rs = -13rs
(-13rs + 20r2 + -21s2) = 0

Solving
-13rs + 20r2 + -21s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5r + -7s)(4r + 3s) = 0


Subproblem 1
Set the factor '(5r + -7s)' equal to zero and attempt to solve:

Simplifying
5r + -7s = 0

Solving
5r + -7s = 0

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

Add '7s' to each side of the equation.
5r + -7s + 7s = 0 + 7s

Combine like terms: -7s + 7s = 0
5r + 0 = 0 + 7s
5r = 0 + 7s
Remove the zero:
5r = 7s

Divide each side by '5'.
r = 1.4s

Simplifying
r = 1.4s

Subproblem 2
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
Solution
r = {1.4s, -0.75s}

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