0=16t^2+24t+5

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Solution for 0=16t^2+24t+5 equation:


Simplifying
0 = 16t2 + 24t + 5

Reorder the terms:
0 = 5 + 24t + 16t2

Solving
0 = 5 + 24t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -24t + -16t2 = 5 + 24t + 16t2 + -5 + -24t + -16t2

Reorder the terms:
-5 + -24t + -16t2 = 5 + -5 + 24t + -24t + 16t2 + -16t2

Combine like terms: 5 + -5 = 0
-5 + -24t + -16t2 = 0 + 24t + -24t + 16t2 + -16t2
-5 + -24t + -16t2 = 24t + -24t + 16t2 + -16t2

Combine like terms: 24t + -24t = 0
-5 + -24t + -16t2 = 0 + 16t2 + -16t2
-5 + -24t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-5 + -24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 24t + 16t2) = 0

Factor a trinomial.
-1((5 + 4t)(1 + 4t)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + 4t)' equal to zero and attempt to solve: Simplifying 5 + 4t = 0 Solving 5 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t = 0 + -5 4t = 0 + -5 Combine like terms: 0 + -5 = -5 4t = -5 Divide each side by '4'. t = -1.25 Simplifying t = -1.25

Subproblem 2

Set the factor '(1 + 4t)' equal to zero and attempt to solve: Simplifying 1 + 4t = 0 Solving 1 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4t = 0 + -1 4t = 0 + -1 Combine like terms: 0 + -1 = -1 4t = -1 Divide each side by '4'. t = -0.25 Simplifying t = -0.25

Solution

t = {-1.25, -0.25}

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