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Simplifying 0 = (-2t + 10)(8t + 4) Reorder the terms: 0 = (10 + -2t)(8t + 4) Reorder the terms: 0 = (10 + -2t)(4 + 8t) Multiply (10 + -2t) * (4 + 8t) 0 = (10(4 + 8t) + -2t * (4 + 8t)) 0 = ((4 * 10 + 8t * 10) + -2t * (4 + 8t)) 0 = ((40 + 80t) + -2t * (4 + 8t)) 0 = (40 + 80t + (4 * -2t + 8t * -2t)) 0 = (40 + 80t + (-8t + -16t2)) Combine like terms: 80t + -8t = 72t 0 = (40 + 72t + -16t2) Solving 0 = 40 + 72t + -16t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -72t + 16t2 = 40 + 72t + -16t2 + -40 + -72t + 16t2 Reorder the terms: -40 + -72t + 16t2 = 40 + -40 + 72t + -72t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 -40 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 -40 + -72t + 16t2 = 0 + -16t2 + 16t2 -40 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -72t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + -9t + 2t2) = 0 Factor a trinomial. 8((-1 + -2t)(5 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-0.5, 5}
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