(3t+2q)(7t-9q)=0

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Solution for (3t+2q)(7t-9q)=0 equation: 


Simplifying
(3t + 2q)(7t + -9q) = 0

Reorder the terms:
(2q + 3t)(7t + -9q) = 0

Reorder the terms:
(2q + 3t)(-9q + 7t) = 0

Multiply (2q + 3t) * (-9q + 7t)
(2q * (-9q + 7t) + 3t * (-9q + 7t)) = 0
((-9q * 2q + 7t * 2q) + 3t * (-9q + 7t)) = 0

Reorder the terms:
((14qt + -18q2) + 3t * (-9q + 7t)) = 0
((14qt + -18q2) + 3t * (-9q + 7t)) = 0
(14qt + -18q2 + (-9q * 3t + 7t * 3t)) = 0
(14qt + -18q2 + (-27qt + 21t2)) = 0

Reorder the terms:
(14qt + -27qt + -18q2 + 21t2) = 0

Combine like terms: 14qt + -27qt = -13qt
(-13qt + -18q2 + 21t2) = 0

Solving
-13qt + -18q2 + 21t2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-2q + -3t)(9q + -7t) = 0


Subproblem 1
Set the factor '(-2q + -3t)' equal to zero and attempt to solve:

Simplifying
-2q + -3t = 0

Solving
-2q + -3t = 0

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

Add '3t' to each side of the equation.
-2q + -3t + 3t = 0 + 3t

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

Divide each side by '-2'.
q = -1.5t

Simplifying
q = -1.5t

Subproblem 2
Set the factor '(9q + -7t)' equal to zero and attempt to solve:

Simplifying
9q + -7t = 0

Solving
9q + -7t = 0

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

Add '7t' to each side of the equation.
9q + -7t + 7t = 0 + 7t

Combine like terms: -7t + 7t = 0
9q + 0 = 0 + 7t
9q = 0 + 7t
Remove the zero:
9q = 7t

Divide each side by '9'.
q = 0.7777777778t

Simplifying
q = 0.7777777778t
Solution
q = {-1.5t, 0.7777777778t}

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