0=-16t^2+208t+480

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Solution for 0=-16t^2+208t+480 equation:


Simplifying
0 = -16t2 + 208t + 480

Reorder the terms:
0 = 480 + 208t + -16t2

Solving
0 = 480 + 208t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -480 = -480
-480 + -208t + 16t2 = 480 + 208t + -16t2 + -480 + -208t + 16t2

Reorder the terms:
-480 + -208t + 16t2 = 480 + -480 + 208t + -208t + -16t2 + 16t2

Combine like terms: 480 + -480 = 0
-480 + -208t + 16t2 = 0 + 208t + -208t + -16t2 + 16t2
-480 + -208t + 16t2 = 208t + -208t + -16t2 + 16t2

Combine like terms: 208t + -208t = 0
-480 + -208t + 16t2 = 0 + -16t2 + 16t2
-480 + -208t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-480 + -208t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-30 + -13t + t2) = 0

Factor a trinomial.
16((-2 + -1t)(15 + -1t)) = 0

Ignore the factor 16.

Subproblem 1

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

Subproblem 2

Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15

Solution

t = {-2, 15}

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