t^2-28t+86=-74

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Solution for t^2-28t+86=-74 equation:


Simplifying
t2 + -28t + 86 = -74

Reorder the terms:
86 + -28t + t2 = -74

Solving
86 + -28t + t2 = -74

Solving for variable 't'.

Reorder the terms:
86 + 74 + -28t + t2 = -74 + 74

Combine like terms: 86 + 74 = 160
160 + -28t + t2 = -74 + 74

Combine like terms: -74 + 74 = 0
160 + -28t + t2 = 0

Factor a trinomial.
(8 + -1t)(20 + -1t) = 0

Subproblem 1

Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8

Subproblem 2

Set the factor '(20 + -1t)' equal to zero and attempt to solve: Simplifying 20 + -1t = 0 Solving 20 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1t = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1t = 0 + -20 -1t = 0 + -20 Combine like terms: 0 + -20 = -20 -1t = -20 Divide each side by '-1'. t = 20 Simplifying t = 20

Solution

t = {8, 20}

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