12v^2+13vr-35r^2=0

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Solution for 12v^2+13vr-35r^2=0 equation:


Simplifying
12v2 + 13vr + -35r2 = 0

Reorder the terms:
13rv + -35r2 + 12v2 = 0

Solving
13rv + -35r2 + 12v2 = 0

Solving for variable 'r'.

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

Subproblem 1

Set the factor '(-7r + -3v)' equal to zero and attempt to solve: Simplifying -7r + -3v = 0 Solving -7r + -3v = 0 Move all terms containing r to the left, all other terms to the right. Add '3v' to each side of the equation. -7r + -3v + 3v = 0 + 3v Combine like terms: -3v + 3v = 0 -7r + 0 = 0 + 3v -7r = 0 + 3v Remove the zero: -7r = 3v Divide each side by '-7'. r = -0.4285714286v Simplifying r = -0.4285714286v

Subproblem 2

Set the factor '(5r + -4v)' equal to zero and attempt to solve: Simplifying 5r + -4v = 0 Solving 5r + -4v = 0 Move all terms containing r to the left, all other terms to the right. Add '4v' to each side of the equation. 5r + -4v + 4v = 0 + 4v Combine like terms: -4v + 4v = 0 5r + 0 = 0 + 4v 5r = 0 + 4v Remove the zero: 5r = 4v Divide each side by '5'. r = 0.8v Simplifying r = 0.8v

Solution

r = {-0.4285714286v, 0.8v}

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