9=10t-t^2

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Solution for 9=10t-t^2 equation:


Simplifying
9 = 10t + -1t2

Solving
9 = 10t + -1t2

Solving for variable 't'.

Reorder the terms:
9 + -10t + t2 = 10t + -10t + -1t2 + t2

Combine like terms: 10t + -10t = 0
9 + -10t + t2 = 0 + -1t2 + t2
9 + -10t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
9 + -10t + t2 = 0

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

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 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9

Solution

t = {1, 9}

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