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Simplifying -16t2 + 32t + 48 = 48 Reorder the terms: 48 + 32t + -16t2 = 48 Add '-48' to each side of the equation. 48 + 32t + -48 + -16t2 = 48 + -48 Reorder the terms: 48 + -48 + 32t + -16t2 = 48 + -48 Combine like terms: 48 + -48 = 0 0 + 32t + -16t2 = 48 + -48 32t + -16t2 = 48 + -48 Combine like terms: 48 + -48 = 0 32t + -16t2 = 0 Solving 32t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16t'. 16t(2 + -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 = 0Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0, 2}
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