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Simplifying 5((3 + -1t)(4 + t)) = 0 Multiply (3 + -1t) * (4 + t) 5((3(4 + t) + -1t * (4 + t))) = 0 5(((4 * 3 + t * 3) + -1t * (4 + t))) = 0 5(((12 + 3t) + -1t * (4 + t))) = 0 5((12 + 3t + (4 * -1t + t * -1t))) = 0 5((12 + 3t + (-4t + -1t2))) = 0 Combine like terms: 3t + -4t = -1t 5((12 + -1t + -1t2)) = 0 (12 * 5 + -1t * 5 + -1t2 * 5) = 0 (60 + -5t + -5t2) = 0 Solving 60 + -5t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(12 + -1t + -1t2) = 0 Factor a trinomial. 5((3 + -1t)(4 + t)) = 0 Ignore the factor 5.Subproblem 1
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 2
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Solution
t = {3, -4}
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