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Simplifying t(4t + -3) + -1(4t + -3)(t + -3) = 0 Reorder the terms: t(-3 + 4t) + -1(4t + -3)(t + -3) = 0 (-3 * t + 4t * t) + -1(4t + -3)(t + -3) = 0 (-3t + 4t2) + -1(4t + -3)(t + -3) = 0 Reorder the terms: -3t + 4t2 + -1(-3 + 4t)(t + -3) = 0 Reorder the terms: -3t + 4t2 + -1(-3 + 4t)(-3 + t) = 0 Multiply (-3 + 4t) * (-3 + t) -3t + 4t2 + -1(-3(-3 + t) + 4t * (-3 + t)) = 0 -3t + 4t2 + -1((-3 * -3 + t * -3) + 4t * (-3 + t)) = 0 -3t + 4t2 + -1((9 + -3t) + 4t * (-3 + t)) = 0 -3t + 4t2 + -1(9 + -3t + (-3 * 4t + t * 4t)) = 0 -3t + 4t2 + -1(9 + -3t + (-12t + 4t2)) = 0 Combine like terms: -3t + -12t = -15t -3t + 4t2 + -1(9 + -15t + 4t2) = 0 -3t + 4t2 + (9 * -1 + -15t * -1 + 4t2 * -1) = 0 -3t + 4t2 + (-9 + 15t + -4t2) = 0 Reorder the terms: -9 + -3t + 15t + 4t2 + -4t2 = 0 Combine like terms: -3t + 15t = 12t -9 + 12t + 4t2 + -4t2 = 0 Combine like terms: 4t2 + -4t2 = 0 -9 + 12t + 0 = 0 -9 + 12t = 0 Solving -9 + 12t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 12t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 12t = 0 + 9 12t = 0 + 9 Combine like terms: 0 + 9 = 9 12t = 9 Divide each side by '12'. t = 0.75 Simplifying t = 0.75
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