v^2+4vp-21p^2=0

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Solution for v^2+4vp-21p^2=0 equation:


Simplifying
v2 + 4vp + -21p2 = 0

Reorder the terms:
4pv + -21p2 + v2 = 0

Solving
4pv + -21p2 + v2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-7p + -1v)(3p + -1v) = 0

Subproblem 1

Set the factor '(-7p + -1v)' equal to zero and attempt to solve: Simplifying -7p + -1v = 0 Solving -7p + -1v = 0 Move all terms containing p to the left, all other terms to the right. Add 'v' to each side of the equation. -7p + -1v + v = 0 + v Combine like terms: -1v + v = 0 -7p + 0 = 0 + v -7p = 0 + v Remove the zero: -7p = v Divide each side by '-7'. p = -0.1428571429v Simplifying p = -0.1428571429v

Subproblem 2

Set the factor '(3p + -1v)' equal to zero and attempt to solve: Simplifying 3p + -1v = 0 Solving 3p + -1v = 0 Move all terms containing p to the left, all other terms to the right. Add 'v' to each side of the equation. 3p + -1v + v = 0 + v Combine like terms: -1v + v = 0 3p + 0 = 0 + v 3p = 0 + v Remove the zero: 3p = v Divide each side by '3'. p = 0.3333333333v Simplifying p = 0.3333333333v

Solution

p = {-0.1428571429v, 0.3333333333v}

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