14=-16t^2+20t+50

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Solution for 14=-16t^2+20t+50 equation:


Simplifying
14 = -16t2 + 20t + 50

Reorder the terms:
14 = 50 + 20t + -16t2

Solving
14 = 50 + 20t + -16t2

Solving for variable 't'.

Combine like terms: 14 + -50 = -36
-36 + -20t + 16t2 = 50 + 20t + -16t2 + -50 + -20t + 16t2

Reorder the terms:
-36 + -20t + 16t2 = 50 + -50 + 20t + -20t + -16t2 + 16t2

Combine like terms: 50 + -50 = 0
-36 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2
-36 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2

Combine like terms: 20t + -20t = 0
-36 + -20t + 16t2 = 0 + -16t2 + 16t2
-36 + -20t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-36 + -20t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -5t + 4t2) = 0

Factor a trinomial.
4((-1 + -1t)(9 + -4t)) = 0

Ignore the factor 4.

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 '(9 + -4t)' equal to zero and attempt to solve: Simplifying 9 + -4t = 0 Solving 9 + -4t = 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 + -4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4t = 0 + -9 -4t = 0 + -9 Combine like terms: 0 + -9 = -9 -4t = -9 Divide each side by '-4'. t = 2.25 Simplifying t = 2.25

Solution

t = {-1, 2.25}

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