36=-16t^2+64t+8

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Solution for 36=-16t^2+64t+8 equation:


Simplifying
36 = -16t2 + 64t + 8

Reorder the terms:
36 = 8 + 64t + -16t2

Solving
36 = 8 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 36 + -8 = 28
28 + -64t + 16t2 = 8 + 64t + -16t2 + -8 + -64t + 16t2

Reorder the terms:
28 + -64t + 16t2 = 8 + -8 + 64t + -64t + -16t2 + 16t2

Combine like terms: 8 + -8 = 0
28 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
28 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
28 + -64t + 16t2 = 0 + -16t2 + 16t2
28 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
28 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -16t + 4t2) = 0

Factor a trinomial.
4((1 + -2t)(7 + -2t)) = 0

Ignore the factor 4.

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 '(7 + -2t)' equal to zero and attempt to solve:

Simplifying
7 + -2t = 0

Solving
7 + -2t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2t = 0 + -7
-2t = 0 + -7

Combine like terms: 0 + -7 = -7
-2t = -7

Divide each side by '-2'.
t = 3.5

Simplifying
t = 3.5
Solution
t = {0.5, 3.5}

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