6p^2+17pq-14q^2=0

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Solution for 6p^2+17pq-14q^2=0 equation: 


Simplifying
6p2 + 17pq + -14q2 = 0

Reorder the terms:
17pq + 6p2 + -14q2 = 0

Solving
17pq + 6p2 + -14q2 = 0

Solving for variable 'p'.

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


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

Simplifying
3p + -2q = 0

Solving
3p + -2q = 0

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

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

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

Divide each side by '3'.
p = 0.6666666667q

Simplifying
p = 0.6666666667q

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

Simplifying
2p + 7q = 0

Solving
2p + 7q = 0

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

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

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

Divide each side by '2'.
p = -3.5q

Simplifying
p = -3.5q
Solution
p = {0.6666666667q, -3.5q}

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