20(t)=5t^2-30t+45

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Solution for 20(t)=5t^2-30t+45 equation:


Simplifying
20(t) = 5t2 + -30t + 45

Reorder the terms:
20t = 45 + -30t + 5t2

Solving
20t = 45 + -30t + 5t2

Solving for variable 't'.

Reorder the terms:
-45 + 20t + 30t + -5t2 = 45 + -30t + 5t2 + -45 + 30t + -5t2

Combine like terms: 20t + 30t = 50t
-45 + 50t + -5t2 = 45 + -30t + 5t2 + -45 + 30t + -5t2

Reorder the terms:
-45 + 50t + -5t2 = 45 + -45 + -30t + 30t + 5t2 + -5t2

Combine like terms: 45 + -45 = 0
-45 + 50t + -5t2 = 0 + -30t + 30t + 5t2 + -5t2
-45 + 50t + -5t2 = -30t + 30t + 5t2 + -5t2

Combine like terms: -30t + 30t = 0
-45 + 50t + -5t2 = 0 + 5t2 + -5t2
-45 + 50t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-45 + 50t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 10t + -1t2) = 0

Factor a trinomial.
5((-9 + t)(1 + -1t)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 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 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9

Subproblem 2

Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1

Solution

t = {9, 1}

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