0=-16t^2+27t+10

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Solution for 0=-16t^2+27t+10 equation:


Simplifying
0 = -16t2 + 27t + 10

Reorder the terms:
0 = 10 + 27t + -16t2

Solving
0 = 10 + 27t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -10 = -10
-10 + -27t + 16t2 = 10 + 27t + -16t2 + -10 + -27t + 16t2

Reorder the terms:
-10 + -27t + 16t2 = 10 + -10 + 27t + -27t + -16t2 + 16t2

Combine like terms: 10 + -10 = 0
-10 + -27t + 16t2 = 0 + 27t + -27t + -16t2 + 16t2
-10 + -27t + 16t2 = 27t + -27t + -16t2 + 16t2

Combine like terms: 27t + -27t = 0
-10 + -27t + 16t2 = 0 + -16t2 + 16t2
-10 + -27t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-10 + -27t + 16t2 = 0

Factor a trinomial.
(-5 + -16t)(2 + -1t) = 0

Subproblem 1

Set the factor '(-5 + -16t)' equal to zero and attempt to solve: Simplifying -5 + -16t = 0 Solving -5 + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -16t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -16t = 0 + 5 -16t = 0 + 5 Combine like terms: 0 + 5 = 5 -16t = 5 Divide each side by '-16'. t = -0.3125 Simplifying t = -0.3125

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 = {-0.3125, 2}

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