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Simplifying (5t + -2t2)(5 + -4t) = 0 Multiply (5t + -2t2) * (5 + -4t) (5t * (5 + -4t) + -2t2 * (5 + -4t)) = 0 ((5 * 5t + -4t * 5t) + -2t2 * (5 + -4t)) = 0 ((25t + -20t2) + -2t2 * (5 + -4t)) = 0 (25t + -20t2 + (5 * -2t2 + -4t * -2t2)) = 0 (25t + -20t2 + (-10t2 + 8t3)) = 0 Combine like terms: -20t2 + -10t2 = -30t2 (25t + -30t2 + 8t3) = 0 Solving 25t + -30t2 + 8t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(25 + -30t + 8t2) = 0 Factor a trinomial. t((5 + -4t)(5 + -2t)) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 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 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Subproblem 3
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {0, 1.25, 2.5}
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