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Simplifying 0 = -5t2 + 36t + 32 Reorder the terms: 0 = 32 + 36t + -5t2 Solving 0 = 32 + 36t + -5t2 Solving for variable 't'. Combine like terms: 0 + -32 = -32 -32 + -36t + 5t2 = 32 + 36t + -5t2 + -32 + -36t + 5t2 Reorder the terms: -32 + -36t + 5t2 = 32 + -32 + 36t + -36t + -5t2 + 5t2 Combine like terms: 32 + -32 = 0 -32 + -36t + 5t2 = 0 + 36t + -36t + -5t2 + 5t2 -32 + -36t + 5t2 = 36t + -36t + -5t2 + 5t2 Combine like terms: 36t + -36t = 0 -32 + -36t + 5t2 = 0 + -5t2 + 5t2 -32 + -36t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -32 + -36t + 5t2 = 0 Factor a trinomial. (-4 + -5t)(8 + -1t) = 0Subproblem 1
Set the factor '(-4 + -5t)' equal to zero and attempt to solve: Simplifying -4 + -5t = 0 Solving -4 + -5t = 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 + -5t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5t = 0 + 4 -5t = 0 + 4 Combine like terms: 0 + 4 = 4 -5t = 4 Divide each side by '-5'. t = -0.8 Simplifying t = -0.8Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-0.8, 8}
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