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Simplifying 5t(t + -3) + -8 = 5(t + -3)(t + 3) Reorder the terms: 5t(-3 + t) + -8 = 5(t + -3)(t + 3) (-3 * 5t + t * 5t) + -8 = 5(t + -3)(t + 3) (-15t + 5t2) + -8 = 5(t + -3)(t + 3) Reorder the terms: -8 + -15t + 5t2 = 5(t + -3)(t + 3) Reorder the terms: -8 + -15t + 5t2 = 5(-3 + t)(t + 3) Reorder the terms: -8 + -15t + 5t2 = 5(-3 + t)(3 + t) Multiply (-3 + t) * (3 + t) -8 + -15t + 5t2 = 5(-3(3 + t) + t(3 + t)) -8 + -15t + 5t2 = 5((3 * -3 + t * -3) + t(3 + t)) -8 + -15t + 5t2 = 5((-9 + -3t) + t(3 + t)) -8 + -15t + 5t2 = 5(-9 + -3t + (3 * t + t * t)) -8 + -15t + 5t2 = 5(-9 + -3t + (3t + t2)) Combine like terms: -3t + 3t = 0 -8 + -15t + 5t2 = 5(-9 + 0 + t2) -8 + -15t + 5t2 = 5(-9 + t2) -8 + -15t + 5t2 = (-9 * 5 + t2 * 5) -8 + -15t + 5t2 = (-45 + 5t2) Add '-5t2' to each side of the equation. -8 + -15t + 5t2 + -5t2 = -45 + 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -8 + -15t + 0 = -45 + 5t2 + -5t2 -8 + -15t = -45 + 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -8 + -15t = -45 + 0 -8 + -15t = -45 Solving -8 + -15t = -45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -15t = -45 + 8 Combine like terms: -8 + 8 = 0 0 + -15t = -45 + 8 -15t = -45 + 8 Combine like terms: -45 + 8 = -37 -15t = -37 Divide each side by '-15'. t = 2.466666667 Simplifying t = 2.466666667
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