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Simplifying -15(t2 + 10t + 21) = 0 Reorder the terms: -15(21 + 10t + t2) = 0 (21 * -15 + 10t * -15 + t2 * -15) = 0 (-315 + -150t + -15t2) = 0 Solving -315 + -150t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-15'. -15(21 + 10t + t2) = 0 Factor a trinomial. -15((7 + t)(3 + t)) = 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 + 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 = {-7, -3}
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