288-16t^2+48t=288

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Solution for 288-16t^2+48t=288 equation:


Simplifying
288 + -16t2 + 48t = 288

Reorder the terms:
288 + 48t + -16t2 = 288

Add '-288' to each side of the equation.
288 + 48t + -288 + -16t2 = 288 + -288

Reorder the terms:
288 + -288 + 48t + -16t2 = 288 + -288

Combine like terms: 288 + -288 = 0
0 + 48t + -16t2 = 288 + -288
48t + -16t2 = 288 + -288

Combine like terms: 288 + -288 = 0
48t + -16t2 = 0

Solving
48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16t'.
16t(3 + -1t) = 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 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3

Solution

t = {0, 3}

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