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Simplifying 15t2 + 135t + 210 = 0 Reorder the terms: 210 + 135t + 15t2 = 0 Solving 210 + 135t + 15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(14 + 9t + t2) = 0 Factor a trinomial. 15((7 + t)(2 + 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 '(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 = -2Solution
t = {-7, -2}
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