12=-16t^2+24t+4

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Solution for 12=-16t^2+24t+4 equation: 


Simplifying
12 = -16t2 + 24t + 4

Reorder the terms:
12 = 4 + 24t + -16t2

Solving
12 = 4 + 24t + -16t2

Solving for variable 't'.

Combine like terms: 12 + -4 = 8
8 + -24t + 16t2 = 4 + 24t + -16t2 + -4 + -24t + 16t2

Reorder the terms:
8 + -24t + 16t2 = 4 + -4 + 24t + -24t + -16t2 + 16t2

Combine like terms: 4 + -4 = 0
8 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2
8 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2

Combine like terms: 24t + -24t = 0
8 + -24t + 16t2 = 0 + -16t2 + 16t2
8 + -24t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
8 + -24t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -3t + 2t2) = 0

Factor a trinomial.
8((1 + -2t)(1 + -1t)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5

Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = 0 + -1
-1t = 0 + -1

Combine like terms: 0 + -1 = -1
-1t = -1

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {0.5, 1}

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