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Simplifying 15t + -5t2 = 10 Solving 15t + -5t2 = 10 Solving for variable 't'. Reorder the terms: -10 + 15t + -5t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 15t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 3t + -1t2) = 0 Factor a trinomial. 5((-2 + t)(1 + -1t)) = 0 Ignore the factor 5.Subproblem 1
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 = 2Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {2, 1}
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