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Simplifying t(t + -3)(t + 4) = 0 Reorder the terms: t(-3 + t)(t + 4) = 0 Reorder the terms: t(-3 + t)(4 + t) = 0 Multiply (-3 + t) * (4 + t) t(-3(4 + t) + t(4 + t)) = 0 t((4 * -3 + t * -3) + t(4 + t)) = 0 t((-12 + -3t) + t(4 + t)) = 0 t(-12 + -3t + (4 * t + t * t)) = 0 t(-12 + -3t + (4t + t2)) = 0 Combine like terms: -3t + 4t = 1t t(-12 + 1t + t2) = 0 (-12 * t + 1t * t + t2 * t) = 0 (-12t + 1t2 + t3) = 0 Solving -12t + 1t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-12 + t + t2) = 0 Factor a trinomial. t((-4 + -1t)(3 + -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 '(-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 = -4Subproblem 3
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 = {0, -4, 3}
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