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Simplifying 2(2t + -2)(3t + 5) = 0 Reorder the terms: 2(-2 + 2t)(3t + 5) = 0 Reorder the terms: 2(-2 + 2t)(5 + 3t) = 0 Multiply (-2 + 2t) * (5 + 3t) 2(-2(5 + 3t) + 2t * (5 + 3t)) = 0 2((5 * -2 + 3t * -2) + 2t * (5 + 3t)) = 0 2((-10 + -6t) + 2t * (5 + 3t)) = 0 2(-10 + -6t + (5 * 2t + 3t * 2t)) = 0 2(-10 + -6t + (10t + 6t2)) = 0 Combine like terms: -6t + 10t = 4t 2(-10 + 4t + 6t2) = 0 (-10 * 2 + 4t * 2 + 6t2 * 2) = 0 (-20 + 8t + 12t2) = 0 Solving -20 + 8t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 2t + 3t2) = 0 Factor a trinomial. 4((-5 + -3t)(1 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -3t)' equal to zero and attempt to solve: Simplifying -5 + -3t = 0 Solving -5 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3t = 0 + 5 -3t = 0 + 5 Combine like terms: 0 + 5 = 5 -3t = 5 Divide each side by '-3'. t = -1.666666667 Simplifying t = -1.666666667Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-1.666666667, 1}
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