t^2+7t-35=2t-11

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Solution for t^2+7t-35=2t-11 equation:


Simplifying
t2 + 7t + -35 = 2t + -11

Reorder the terms:
-35 + 7t + t2 = 2t + -11

Reorder the terms:
-35 + 7t + t2 = -11 + 2t

Solving
-35 + 7t + t2 = -11 + 2t

Solving for variable 't'.

Reorder the terms:
-35 + 11 + 7t + -2t + t2 = -11 + 2t + 11 + -2t

Combine like terms: -35 + 11 = -24
-24 + 7t + -2t + t2 = -11 + 2t + 11 + -2t

Combine like terms: 7t + -2t = 5t
-24 + 5t + t2 = -11 + 2t + 11 + -2t

Reorder the terms:
-24 + 5t + t2 = -11 + 11 + 2t + -2t

Combine like terms: -11 + 11 = 0
-24 + 5t + t2 = 0 + 2t + -2t
-24 + 5t + t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-24 + 5t + t2 = 0

Factor a trinomial.
(-8 + -1t)(3 + -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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3

Solution

t = {-8, 3}

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