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Simplifying t(t + 3)(t + -15) = 0 Reorder the terms: t(3 + t)(t + -15) = 0 Reorder the terms: t(3 + t)(-15 + t) = 0 Multiply (3 + t) * (-15 + t) t(3(-15 + t) + t(-15 + t)) = 0 t((-15 * 3 + t * 3) + t(-15 + t)) = 0 t((-45 + 3t) + t(-15 + t)) = 0 t(-45 + 3t + (-15 * t + t * t)) = 0 t(-45 + 3t + (-15t + t2)) = 0 Combine like terms: 3t + -15t = -12t t(-45 + -12t + t2) = 0 (-45 * t + -12t * t + t2 * t) = 0 (-45t + -12t2 + t3) = 0 Solving -45t + -12t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-45 + -12t + t2) = 0 Factor a trinomial. t((-3 + -1t)(15 + -1t)) = 0Subproblem 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 + -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 = -3Subproblem 3
Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15Solution
t = {0, -3, 15}
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