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Simplifying (3t + -10)(t + -2) = 0 Reorder the terms: (-10 + 3t)(t + -2) = 0 Reorder the terms: (-10 + 3t)(-2 + t) = 0 Multiply (-10 + 3t) * (-2 + t) (-10(-2 + t) + 3t * (-2 + t)) = 0 ((-2 * -10 + t * -10) + 3t * (-2 + t)) = 0 ((20 + -10t) + 3t * (-2 + t)) = 0 (20 + -10t + (-2 * 3t + t * 3t)) = 0 (20 + -10t + (-6t + 3t2)) = 0 Combine like terms: -10t + -6t = -16t (20 + -16t + 3t2) = 0 Solving 20 + -16t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (2 + -1t)(10 + -3t) = 0Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(10 + -3t)' equal to zero and attempt to solve: Simplifying 10 + -3t = 0 Solving 10 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3t = 0 + -10 -3t = 0 + -10 Combine like terms: 0 + -10 = -10 -3t = -10 Divide each side by '-3'. t = 3.333333333 Simplifying t = 3.333333333Solution
t = {2, 3.333333333}
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