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Simplifying [(t2 + 3t + -8) + -1(t2 + -2t + 6)](t + -4) = 0 Reorder the terms: [(-8 + 3t + t2) + -1(t2 + -2t + 6)](t + -4) = 0 Remove parenthesis around (-8 + 3t + t2) [-8 + 3t + t2 + -1(t2 + -2t + 6)](t + -4) = 0 Reorder the terms: [-8 + 3t + t2 + -1(6 + -2t + t2)](t + -4) = 0 [-8 + 3t + t2 + (6 * -1 + -2t * -1 + t2 * -1)](t + -4) = 0 [-8 + 3t + t2 + (-6 + 2t + -1t2)](t + -4) = 0 Reorder the terms: [-8 + -6 + 3t + 2t + t2 + -1t2](t + -4) = 0 Combine like terms: -8 + -6 = -14 [-14 + 3t + 2t + t2 + -1t2](t + -4) = 0 Combine like terms: 3t + 2t = 5t [-14 + 5t + t2 + -1t2](t + -4) = 0 Combine like terms: t2 + -1t2 = 0 [-14 + 5t + 0](t + -4) = 0 [-14 + 5t](t + -4) = 0 Reorder the terms: [-14 + 5t](-4 + t) = 0 Multiply [-14 + 5t] * (-4 + t) [-14(-4 + t) + 5t * (-4 + t)] = 0 [(-4 * -14 + t * -14) + 5t * (-4 + t)] = 0 [(56 + -14t) + 5t * (-4 + t)] = 0 [56 + -14t + (-4 * 5t + t * 5t)] = 0 [56 + -14t + (-20t + 5t2)] = 0 Combine like terms: -14t + -20t = -34t [56 + -34t + 5t2] = 0 Solving 56 + -34t + 5t2 = 0 Solving for variable 't'. Factor a trinomial. (14 + -5t)(4 + -1t) = 0Subproblem 1
Set the factor '(14 + -5t)' equal to zero and attempt to solve: Simplifying 14 + -5t = 0 Solving 14 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -5t = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -5t = 0 + -14 -5t = 0 + -14 Combine like terms: 0 + -14 = -14 -5t = -14 Divide each side by '-5'. t = 2.8 Simplifying t = 2.8Subproblem 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 = 4Solution
t = {2.8, 4}
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