(3r-5v)(7r+4v)=

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


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

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

Reorder the terms:
((12rv + 21r2) + -5v * (7r + 4v)) = 0
((12rv + 21r2) + -5v * (7r + 4v)) = 0
(12rv + 21r2 + (7r * -5v + 4v * -5v)) = 0
(12rv + 21r2 + (-35rv + -20v2)) = 0

Reorder the terms:
(12rv + -35rv + 21r2 + -20v2) = 0

Combine like terms: 12rv + -35rv = -23rv
(-23rv + 21r2 + -20v2) = 0

Solving
-23rv + 21r2 + -20v2 = 0

Solving for variable 'r'.

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


Subproblem 1
Set the factor '(3r + -5v)' equal to zero and attempt to solve:

Simplifying
3r + -5v = 0

Solving
3r + -5v = 0

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

Add '5v' to each side of the equation.
3r + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
3r + 0 = 0 + 5v
3r = 0 + 5v
Remove the zero:
3r = 5v

Divide each side by '3'.
r = 1.666666667v

Simplifying
r = 1.666666667v

Subproblem 2
Set the factor '(7r + 4v)' equal to zero and attempt to solve:

Simplifying
7r + 4v = 0

Solving
7r + 4v = 0

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

Add '-4v' to each side of the equation.
7r + 4v + -4v = 0 + -4v

Combine like terms: 4v + -4v = 0
7r + 0 = 0 + -4v
7r = 0 + -4v
Remove the zero:
7r = -4v

Divide each side by '7'.
r = -0.5714285714v

Simplifying
r = -0.5714285714v
Solution
r = {1.666666667v, -0.5714285714v}

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