3=-16t^2+48t+3

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Solution for 3=-16t^2+48t+3 equation:


Simplifying
3 = -16t2 + 48t + 3

Reorder the terms:
3 = 3 + 48t + -16t2

Add '-3' to each side of the equation.
3 + -3 = 3 + 48t + -3 + -16t2

Combine like terms: 3 + -3 = 0
0 = 3 + 48t + -3 + -16t2

Reorder the terms:
0 = 3 + -3 + 48t + -16t2

Combine like terms: 3 + -3 = 0
0 = 0 + 48t + -16t2
0 = 48t + -16t2

Solving
0 = 48t + -16t2

Solving for variable 't'.
Remove the zero:
-48t + 16t2 = 48t + -16t2 + -48t + 16t2

Reorder the terms:
-48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-48t + 16t2 = 0 + -16t2 + 16t2
-48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16t'.
16t(-3 + t) = 0

Ignore the factor 16.

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3

Solution

t = {0, 3}

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