8t^2+5t+18=29t

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Solution for 8t^2+5t+18=29t equation:


Simplifying
8t2 + 5t + 18 = 29t

Reorder the terms:
18 + 5t + 8t2 = 29t

Solving
18 + 5t + 8t2 = 29t

Solving for variable 't'.

Reorder the terms:
18 + 5t + -29t + 8t2 = 29t + -29t

Combine like terms: 5t + -29t = -24t
18 + -24t + 8t2 = 29t + -29t

Combine like terms: 29t + -29t = 0
18 + -24t + 8t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -12t + 4t2) = 0

Factor a trinomial.
2((3 + -2t)(3 + -2t)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5

Subproblem 2

Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5

Solution

t = {1.5, 1.5}

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