17(t-3)(t+8)=0

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Solution for 17(t-3)(t+8)=0 equation: 


Simplifying
17(t + -3)(t + 8) = 0

Reorder the terms:
17(-3 + t)(t + 8) = 0

Reorder the terms:
17(-3 + t)(8 + t) = 0

Multiply (-3 + t) * (8 + t)
17(-3(8 + t) + t(8 + t)) = 0
17((8 * -3 + t * -3) + t(8 + t)) = 0
17((-24 + -3t) + t(8 + t)) = 0
17(-24 + -3t + (8 * t + t * t)) = 0
17(-24 + -3t + (8t + t2)) = 0

Combine like terms: -3t + 8t = 5t
17(-24 + 5t + t2) = 0
(-24 * 17 + 5t * 17 + t2 * 17) = 0
(-408 + 85t + 17t2) = 0

Solving
-408 + 85t + 17t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '17'.
17(-24 + 5t + t2) = 0

Factor a trinomial.
17((-8 + -1t)(3 + -1t)) = 0

Ignore the factor 17.

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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