24=8t+16t^2

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Solution for 24=8t+16t^2 equation:


Simplifying
24 = 8t + 16t2

Solving
24 = 8t + 16t2

Solving for variable 't'.

Reorder the terms:
24 + -8t + -16t2 = 8t + -8t + 16t2 + -16t2

Combine like terms: 8t + -8t = 0
24 + -8t + -16t2 = 0 + 16t2 + -16t2
24 + -8t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
24 + -8t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + -1t + -2t2) = 0

Factor a trinomial.
8((1 + -1t)(3 + 2t)) = 0

Ignore the factor 8.

Subproblem 1

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

Subproblem 2

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

Solution

t = {1, -1.5}

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