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Simplifying 336 = -16t2 + 40t + 672 Reorder the terms: 336 = 672 + 40t + -16t2 Solving 336 = 672 + 40t + -16t2 Solving for variable 't'. Combine like terms: 336 + -672 = -336 -336 + -40t + 16t2 = 672 + 40t + -16t2 + -672 + -40t + 16t2 Reorder the terms: -336 + -40t + 16t2 = 672 + -672 + 40t + -40t + -16t2 + 16t2 Combine like terms: 672 + -672 = 0 -336 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2 -336 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2 Combine like terms: 40t + -40t = 0 -336 + -40t + 16t2 = 0 + -16t2 + 16t2 -336 + -40t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -336 + -40t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-42 + -5t + 2t2) = 0 Factor a trinomial. 8((-7 + -2t)(6 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-7 + -2t)' equal to zero and attempt to solve: Simplifying -7 + -2t = 0 Solving -7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2t = 0 + 7 -2t = 0 + 7 Combine like terms: 0 + 7 = 7 -2t = 7 Divide each side by '-2'. t = -3.5 Simplifying t = -3.5Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-3.5, 6}
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