10=10+32t-16t^2

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Solution for 10=10+32t-16t^2 equation:


Simplifying
10 = 10 + 32t + -16t2

Add '-10' to each side of the equation.
10 + -10 = 10 + 32t + -10 + -16t2

Combine like terms: 10 + -10 = 0
0 = 10 + 32t + -10 + -16t2

Reorder the terms:
0 = 10 + -10 + 32t + -16t2

Combine like terms: 10 + -10 = 0
0 = 0 + 32t + -16t2
0 = 32t + -16t2

Solving
0 = 32t + -16t2

Solving for variable 't'.
Remove the zero:
-32t + 16t2 = 32t + -16t2 + -32t + 16t2

Reorder the terms:
-32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-32t + 16t2 = 0 + -16t2 + 16t2
-32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16t'.
16t(-2 + 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 '(-2 + t)' equal to zero and attempt to solve: Simplifying -2 + t = 0 Solving -2 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2

Solution

t = {0, 2}

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