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Simplifying 9t3 + 15t2 + t + -6 = (t + 3)(t + -2) + -3t3 Reorder the terms: -6 + t + 15t2 + 9t3 = (t + 3)(t + -2) + -3t3 Reorder the terms: -6 + t + 15t2 + 9t3 = (3 + t)(t + -2) + -3t3 Reorder the terms: -6 + t + 15t2 + 9t3 = (3 + t)(-2 + t) + -3t3 Multiply (3 + t) * (-2 + t) -6 + t + 15t2 + 9t3 = (3(-2 + t) + t(-2 + t)) + -3t3 -6 + t + 15t2 + 9t3 = ((-2 * 3 + t * 3) + t(-2 + t)) + -3t3 -6 + t + 15t2 + 9t3 = ((-6 + 3t) + t(-2 + t)) + -3t3 -6 + t + 15t2 + 9t3 = (-6 + 3t + (-2 * t + t * t)) + -3t3 -6 + t + 15t2 + 9t3 = (-6 + 3t + (-2t + t2)) + -3t3 Combine like terms: 3t + -2t = 1t -6 + t + 15t2 + 9t3 = (-6 + 1t + t2) + -3t3 Add '6' to each side of the equation. -6 + t + 15t2 + 6 + 9t3 = -6 + 1t + t2 + 6 + -3t3 Reorder the terms: -6 + 6 + t + 15t2 + 9t3 = -6 + 1t + t2 + 6 + -3t3 Combine like terms: -6 + 6 = 0 0 + t + 15t2 + 9t3 = -6 + 1t + t2 + 6 + -3t3 t + 15t2 + 9t3 = -6 + 1t + t2 + 6 + -3t3 Reorder the terms: t + 15t2 + 9t3 = -6 + 6 + 1t + t2 + -3t3 Combine like terms: -6 + 6 = 0 t + 15t2 + 9t3 = 0 + 1t + t2 + -3t3 t + 15t2 + 9t3 = 1t + t2 + -3t3 Solving t + 15t2 + 9t3 = 1t + t2 + -3t3 Solving for variable 't'. Reorder the terms: t + -1t + 15t2 + -1t2 + 9t3 + 3t3 = 1t + t2 + -3t3 + -1t + -1t2 + 3t3 Combine like terms: t + -1t = 0 0 + 15t2 + -1t2 + 9t3 + 3t3 = 1t + t2 + -3t3 + -1t + -1t2 + 3t3 15t2 + -1t2 + 9t3 + 3t3 = 1t + t2 + -3t3 + -1t + -1t2 + 3t3 Combine like terms: 15t2 + -1t2 = 14t2 14t2 + 9t3 + 3t3 = 1t + t2 + -3t3 + -1t + -1t2 + 3t3 Combine like terms: 9t3 + 3t3 = 12t3 14t2 + 12t3 = 1t + t2 + -3t3 + -1t + -1t2 + 3t3 Reorder the terms: 14t2 + 12t3 = 1t + -1t + t2 + -1t2 + -3t3 + 3t3 Combine like terms: 1t + -1t = 0 14t2 + 12t3 = 0 + t2 + -1t2 + -3t3 + 3t3 14t2 + 12t3 = t2 + -1t2 + -3t3 + 3t3 Combine like terms: t2 + -1t2 = 0 14t2 + 12t3 = 0 + -3t3 + 3t3 14t2 + 12t3 = -3t3 + 3t3 Combine like terms: -3t3 + 3t3 = 0 14t2 + 12t3 = 0 Factor out the Greatest Common Factor (GCF), '2t2'. 2t2(7 + 6t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(7 + 6t)' equal to zero and attempt to solve: Simplifying 7 + 6t = 0 Solving 7 + 6t = 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 + 6t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6t = 0 + -7 6t = 0 + -7 Combine like terms: 0 + -7 = -7 6t = -7 Divide each side by '6'. t = -1.166666667 Simplifying t = -1.166666667Solution
t = {0, -1.166666667}
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