13=-16t^2+30t+4

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Solution for 13=-16t^2+30t+4 equation:


Simplifying
13 = -16t2 + 30t + 4

Reorder the terms:
13 = 4 + 30t + -16t2

Solving
13 = 4 + 30t + -16t2

Solving for variable 't'.

Combine like terms: 13 + -4 = 9
9 + -30t + 16t2 = 4 + 30t + -16t2 + -4 + -30t + 16t2

Reorder the terms:
9 + -30t + 16t2 = 4 + -4 + 30t + -30t + -16t2 + 16t2

Combine like terms: 4 + -4 = 0
9 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2
9 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2

Combine like terms: 30t + -30t = 0
9 + -30t + 16t2 = 0 + -16t2 + 16t2
9 + -30t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
9 + -30t + 16t2 = 0

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

Subproblem 1

Set the factor '(3 + -8t)' equal to zero and attempt to solve: Simplifying 3 + -8t = 0 Solving 3 + -8t = 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 + -8t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8t = 0 + -3 -8t = 0 + -3 Combine like terms: 0 + -3 = -3 -8t = -3 Divide each side by '-8'. t = 0.375 Simplifying t = 0.375

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 = {0.375, 1.5}

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