16a^2-24at+9t^2=0

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Solution for 16a^2-24at+9t^2=0 equation:


Simplifying
16a2 + -24at + 9t2 = 0

Reorder the terms:
-24at + 16a2 + 9t2 = 0

Solving
-24at + 16a2 + 9t2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -3t)(4a + -3t) = 0

Subproblem 1

Set the factor '(4a + -3t)' equal to zero and attempt to solve: Simplifying 4a + -3t = 0 Solving 4a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 4a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 4a + 0 = 0 + 3t 4a = 0 + 3t Remove the zero: 4a = 3t Divide each side by '4'. a = 0.75t Simplifying a = 0.75t

Subproblem 2

Set the factor '(4a + -3t)' equal to zero and attempt to solve: Simplifying 4a + -3t = 0 Solving 4a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 4a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 4a + 0 = 0 + 3t 4a = 0 + 3t Remove the zero: 4a = 3t Divide each side by '4'. a = 0.75t Simplifying a = 0.75t

Solution

a = {0.75t, 0.75t}

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