t^2+3t=-24-8t

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Solution for t^2+3t=-24-8t equation:


Simplifying
t2 + 3t = -24 + -8t

Reorder the terms:
3t + t2 = -24 + -8t

Solving
3t + t2 = -24 + -8t

Solving for variable 't'.

Reorder the terms:
24 + 3t + 8t + t2 = -24 + -8t + 24 + 8t

Combine like terms: 3t + 8t = 11t
24 + 11t + t2 = -24 + -8t + 24 + 8t

Reorder the terms:
24 + 11t + t2 = -24 + 24 + -8t + 8t

Combine like terms: -24 + 24 = 0
24 + 11t + t2 = 0 + -8t + 8t
24 + 11t + t2 = -8t + 8t

Combine like terms: -8t + 8t = 0
24 + 11t + t2 = 0

Factor a trinomial.
(8 + t)(3 + t) = 0

Subproblem 1

Set the factor '(8 + t)' equal to zero and attempt to solve: Simplifying 8 + t = 0 Solving 8 + t = 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 + t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + t = 0 + -8 t = 0 + -8 Combine like terms: 0 + -8 = -8 t = -8 Simplifying t = -8

Subproblem 2

Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3

Solution

t = {-8, -3}

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