30a^2+19at-63t^2=0

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Solution for 30a^2+19at-63t^2=0 equation:


Simplifying
30a2 + 19at + -63t2 = 0

Reorder the terms:
19at + 30a2 + -63t2 = 0

Solving
19at + 30a2 + -63t2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + -7t)(5a + 9t) = 0

Subproblem 1

Set the factor '(6a + -7t)' equal to zero and attempt to solve: Simplifying 6a + -7t = 0 Solving 6a + -7t = 0 Move all terms containing a to the left, all other terms to the right. Add '7t' to each side of the equation. 6a + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 6a + 0 = 0 + 7t 6a = 0 + 7t Remove the zero: 6a = 7t Divide each side by '6'. a = 1.166666667t Simplifying a = 1.166666667t

Subproblem 2

Set the factor '(5a + 9t)' equal to zero and attempt to solve: Simplifying 5a + 9t = 0 Solving 5a + 9t = 0 Move all terms containing a to the left, all other terms to the right. Add '-9t' to each side of the equation. 5a + 9t + -9t = 0 + -9t Combine like terms: 9t + -9t = 0 5a + 0 = 0 + -9t 5a = 0 + -9t Remove the zero: 5a = -9t Divide each side by '5'. a = -1.8t Simplifying a = -1.8t

Solution

a = {1.166666667t, -1.8t}

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