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Simplifying 10 = -5t2 + 15t + 10 Reorder the terms: 10 = 10 + 15t + -5t2 Add '-10' to each side of the equation. 10 + -10 = 10 + 15t + -10 + -5t2 Combine like terms: 10 + -10 = 0 0 = 10 + 15t + -10 + -5t2 Reorder the terms: 0 = 10 + -10 + 15t + -5t2 Combine like terms: 10 + -10 = 0 0 = 0 + 15t + -5t2 0 = 15t + -5t2 Solving 0 = 15t + -5t2 Solving for variable 't'. Remove the zero: -15t + 5t2 = 15t + -5t2 + -15t + 5t2 Reorder the terms: -15t + 5t2 = 15t + -15t + -5t2 + 5t2 Combine like terms: 15t + -15t = 0 -15t + 5t2 = 0 + -5t2 + 5t2 -15t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -15t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(-3 + t) = 0 Ignore the factor 5.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 '(-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 = 3Solution
t = {0, 3}
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