0=4+30t-16t^2

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Solution for 0=4+30t-16t^2 equation:


Simplifying
0 = 4 + 30t + -16t2

Solving
0 = 4 + 30t + -16t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -15t + 8t2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -8t)' equal to zero and attempt to solve: Simplifying -1 + -8t = 0 Solving -1 + -8t = 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 + -8t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8t = 0 + 1 -8t = 0 + 1 Combine like terms: 0 + 1 = 1 -8t = 1 Divide each side by '-8'. t = -0.125 Simplifying t = -0.125

Subproblem 2

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Solution

t = {-0.125, 2}

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