=6v^2+17vp-14p^2

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Solution for =6v^2+17vp-14p^2 equation: 


Simplifying
0 = 6v2 + 17vp + -14p2

Reorder the terms:
0 = 17pv + -14p2 + 6v2

Solving
0 = 17pv + -14p2 + 6v2

Solving for variable 'p'.
Remove the zero:
-17pv + 14p2 + -6v2 = 17pv + -14p2 + 6v2 + -17pv + 14p2 + -6v2

Reorder the terms:
-17pv + 14p2 + -6v2 = 17pv + -17pv + -14p2 + 14p2 + 6v2 + -6v2

Combine like terms: 17pv + -17pv = 0
-17pv + 14p2 + -6v2 = 0 + -14p2 + 14p2 + 6v2 + -6v2
-17pv + 14p2 + -6v2 = -14p2 + 14p2 + 6v2 + -6v2

Combine like terms: -14p2 + 14p2 = 0
-17pv + 14p2 + -6v2 = 0 + 6v2 + -6v2
-17pv + 14p2 + -6v2 = 6v2 + -6v2

Combine like terms: 6v2 + -6v2 = 0
-17pv + 14p2 + -6v2 = 0

Factor a trinomial.
(2p + -3v)(7p + 2v) = 0


Subproblem 1
Set the factor '(2p + -3v)' equal to zero and attempt to solve:

Simplifying
2p + -3v = 0

Solving
2p + -3v = 0

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

Add '3v' to each side of the equation.
2p + -3v + 3v = 0 + 3v

Combine like terms: -3v + 3v = 0
2p + 0 = 0 + 3v
2p = 0 + 3v
Remove the zero:
2p = 3v

Divide each side by '2'.
p = 1.5v

Simplifying
p = 1.5v

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

Simplifying
7p + 2v = 0

Solving
7p + 2v = 0

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

Add '-2v' to each side of the equation.
7p + 2v + -2v = 0 + -2v

Combine like terms: 2v + -2v = 0
7p + 0 = 0 + -2v
7p = 0 + -2v
Remove the zero:
7p = -2v

Divide each side by '7'.
p = -0.2857142857v

Simplifying
p = -0.2857142857v
Solution
p = {1.5v, -0.2857142857v}

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