4a^2-12at+9t^2=0

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Solution for 4a^2-12at+9t^2=0 equation:


Simplifying
4a2 + -12at + 9t2 = 0

Reorder the terms:
-12at + 4a2 + 9t2 = 0

Solving
-12at + 4a2 + 9t2 = 0

Solving for variable 'a'.

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

Subproblem 1

Set the factor '(2a + -3t)' equal to zero and attempt to solve: Simplifying 2a + -3t = 0 Solving 2a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 2a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 2a + 0 = 0 + 3t 2a = 0 + 3t Remove the zero: 2a = 3t Divide each side by '2'. a = 1.5t Simplifying a = 1.5t

Subproblem 2

Set the factor '(2a + -3t)' equal to zero and attempt to solve: Simplifying 2a + -3t = 0 Solving 2a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 2a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 2a + 0 = 0 + 3t 2a = 0 + 3t Remove the zero: 2a = 3t Divide each side by '2'. a = 1.5t Simplifying a = 1.5t

Solution

a = {1.5t, 1.5t}

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