64t=12t^2+45

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Solution for 64t=12t^2+45 equation:


Simplifying
64t = 12t2 + 45

Reorder the terms:
64t = 45 + 12t2

Solving
64t = 45 + 12t2

Solving for variable 't'.

Reorder the terms:
-45 + 64t + -12t2 = 45 + 12t2 + -45 + -12t2

Reorder the terms:
-45 + 64t + -12t2 = 45 + -45 + 12t2 + -12t2

Combine like terms: 45 + -45 = 0
-45 + 64t + -12t2 = 0 + 12t2 + -12t2
-45 + 64t + -12t2 = 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
-45 + 64t + -12t2 = 0

Factor a trinomial.
(-9 + 2t)(5 + -6t) = 0

Subproblem 1

Set the factor '(-9 + 2t)' equal to zero and attempt to solve: Simplifying -9 + 2t = 0 Solving -9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t = 0 + 9 2t = 0 + 9 Combine like terms: 0 + 9 = 9 2t = 9 Divide each side by '2'. t = 4.5 Simplifying t = 4.5

Subproblem 2

Set the factor '(5 + -6t)' equal to zero and attempt to solve: Simplifying 5 + -6t = 0 Solving 5 + -6t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6t = 0 + -5 -6t = 0 + -5 Combine like terms: 0 + -5 = -5 -6t = -5 Divide each side by '-6'. t = 0.8333333333 Simplifying t = 0.8333333333

Solution

t = {4.5, 0.8333333333}

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