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Simplifying -15t2 + 150t + 10 = 325 Reorder the terms: 10 + 150t + -15t2 = 325 Solving 10 + 150t + -15t2 = 325 Solving for variable 't'. Reorder the terms: 10 + -325 + 150t + -15t2 = 325 + -325 Combine like terms: 10 + -325 = -315 -315 + 150t + -15t2 = 325 + -325 Combine like terms: 325 + -325 = 0 -315 + 150t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-21 + 10t + -1t2) = 0 Factor a trinomial. 15((-7 + t)(3 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Subproblem 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 = 3Solution
t = {7, 3}
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