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Simplifying t(4t + 12) = 40 Reorder the terms: t(12 + 4t) = 40 (12 * t + 4t * t) = 40 (12t + 4t2) = 40 Solving 12t + 4t2 = 40 Solving for variable 't'. Reorder the terms: -40 + 12t + 4t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 12t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 3t + t2) = 0 Factor a trinomial. 4((-5 + -1t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
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 = -5Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-5, 2}
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