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Simplifying 7(t2 + 5t + -9) + t = t(7t + -2) + 13 Reorder the terms: 7(-9 + 5t + t2) + t = t(7t + -2) + 13 (-9 * 7 + 5t * 7 + t2 * 7) + t = t(7t + -2) + 13 (-63 + 35t + 7t2) + t = t(7t + -2) + 13 Reorder the terms: -63 + 35t + t + 7t2 = t(7t + -2) + 13 Combine like terms: 35t + t = 36t -63 + 36t + 7t2 = t(7t + -2) + 13 Reorder the terms: -63 + 36t + 7t2 = t(-2 + 7t) + 13 -63 + 36t + 7t2 = (-2 * t + 7t * t) + 13 -63 + 36t + 7t2 = (-2t + 7t2) + 13 Reorder the terms: -63 + 36t + 7t2 = 13 + -2t + 7t2 Add '-7t2' to each side of the equation. -63 + 36t + 7t2 + -7t2 = 13 + -2t + 7t2 + -7t2 Combine like terms: 7t2 + -7t2 = 0 -63 + 36t + 0 = 13 + -2t + 7t2 + -7t2 -63 + 36t = 13 + -2t + 7t2 + -7t2 Combine like terms: 7t2 + -7t2 = 0 -63 + 36t = 13 + -2t + 0 -63 + 36t = 13 + -2t Solving -63 + 36t = 13 + -2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2t' to each side of the equation. -63 + 36t + 2t = 13 + -2t + 2t Combine like terms: 36t + 2t = 38t -63 + 38t = 13 + -2t + 2t Combine like terms: -2t + 2t = 0 -63 + 38t = 13 + 0 -63 + 38t = 13 Add '63' to each side of the equation. -63 + 63 + 38t = 13 + 63 Combine like terms: -63 + 63 = 0 0 + 38t = 13 + 63 38t = 13 + 63 Combine like terms: 13 + 63 = 76 38t = 76 Divide each side by '38'. t = 2 Simplifying t = 2
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