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Simplifying t(t + -4)(t + 9) = 0 Reorder the terms: t(-4 + t)(t + 9) = 0 Reorder the terms: t(-4 + t)(9 + t) = 0 Multiply (-4 + t) * (9 + t) t(-4(9 + t) + t(9 + t)) = 0 t((9 * -4 + t * -4) + t(9 + t)) = 0 t((-36 + -4t) + t(9 + t)) = 0 t(-36 + -4t + (9 * t + t * t)) = 0 t(-36 + -4t + (9t + t2)) = 0 Combine like terms: -4t + 9t = 5t t(-36 + 5t + t2) = 0 (-36 * t + 5t * t + t2 * t) = 0 (-36t + 5t2 + t3) = 0 Solving -36t + 5t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-36 + 5t + t2) = 0 Factor a trinomial. t((-9 + -1t)(4 + -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 '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {0, -9, 4}
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