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Simplifying t(7 + t) = 4(t + 7) (7 * t + t * t) = 4(t + 7) (7t + t2) = 4(t + 7) Reorder the terms: 7t + t2 = 4(7 + t) 7t + t2 = (7 * 4 + t * 4) 7t + t2 = (28 + 4t) Solving 7t + t2 = 28 + 4t Solving for variable 't'. Reorder the terms: -28 + 7t + -4t + t2 = 28 + 4t + -28 + -4t Combine like terms: 7t + -4t = 3t -28 + 3t + t2 = 28 + 4t + -28 + -4t Reorder the terms: -28 + 3t + t2 = 28 + -28 + 4t + -4t Combine like terms: 28 + -28 = 0 -28 + 3t + t2 = 0 + 4t + -4t -28 + 3t + t2 = 4t + -4t Combine like terms: 4t + -4t = 0 -28 + 3t + t2 = 0 Factor a trinomial. (-7 + -1t)(4 + -1t) = 0Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve: Simplifying -7 + -1t = 0 Solving -7 + -1t = 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 + -1t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t = 0 + 7 -1t = 0 + 7 Combine like terms: 0 + 7 = 7 -1t = 7 Divide each side by '-1'. t = -7 Simplifying t = -7Subproblem 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 = {-7, 4}
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