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Simplifying (t2 + -100)(t + -10)(t + 10) = 0 Reorder the terms: (-100 + t2)(t + -10)(t + 10) = 0 Reorder the terms: (-100 + t2)(-10 + t)(t + 10) = 0 Reorder the terms: (-100 + t2)(-10 + t)(10 + t) = 0 Multiply (-100 + t2) * (-10 + t) (-100(-10 + t) + t2(-10 + t))(10 + t) = 0 ((-10 * -100 + t * -100) + t2(-10 + t))(10 + t) = 0 ((1000 + -100t) + t2(-10 + t))(10 + t) = 0 (1000 + -100t + (-10 * t2 + t * t2))(10 + t) = 0 (1000 + -100t + (-10t2 + t3))(10 + t) = 0 (1000 + -100t + -10t2 + t3)(10 + t) = 0 Multiply (1000 + -100t + -10t2 + t3) * (10 + t) (1000(10 + t) + -100t * (10 + t) + -10t2 * (10 + t) + t3(10 + t)) = 0 ((10 * 1000 + t * 1000) + -100t * (10 + t) + -10t2 * (10 + t) + t3(10 + t)) = 0 ((10000 + 1000t) + -100t * (10 + t) + -10t2 * (10 + t) + t3(10 + t)) = 0 (10000 + 1000t + (10 * -100t + t * -100t) + -10t2 * (10 + t) + t3(10 + t)) = 0 (10000 + 1000t + (-1000t + -100t2) + -10t2 * (10 + t) + t3(10 + t)) = 0 (10000 + 1000t + -1000t + -100t2 + (10 * -10t2 + t * -10t2) + t3(10 + t)) = 0 (10000 + 1000t + -1000t + -100t2 + (-100t2 + -10t3) + t3(10 + t)) = 0 (10000 + 1000t + -1000t + -100t2 + -100t2 + -10t3 + (10 * t3 + t * t3)) = 0 (10000 + 1000t + -1000t + -100t2 + -100t2 + -10t3 + (10t3 + t4)) = 0 Combine like terms: 1000t + -1000t = 0 (10000 + 0 + -100t2 + -100t2 + -10t3 + 10t3 + t4) = 0 (10000 + -100t2 + -100t2 + -10t3 + 10t3 + t4) = 0 Combine like terms: -100t2 + -100t2 = -200t2 (10000 + -200t2 + -10t3 + 10t3 + t4) = 0 Combine like terms: -10t3 + 10t3 = 0 (10000 + -200t2 + 0 + t4) = 0 (10000 + -200t2 + t4) = 0 Solving 10000 + -200t2 + t4 = 0 Solving for variable 't'. Factor a trinomial. (100 + -1t2)(100 + -1t2) = 0 Factor a difference between two squares. ((10 + t)(10 + -1t))(100 + -1t2) = 0 Factor a difference between two squares. ((10 + t)(10 + -1t))(10 + t)(10 + -1t) = 0Subproblem 1
Set the factor '(10 + t)' equal to zero and attempt to solve: Simplifying 10 + t = 0 Solving 10 + t = 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 + t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + t = 0 + -10 t = 0 + -10 Combine like terms: 0 + -10 = -10 t = -10 Simplifying t = -10Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 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 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Subproblem 3
Set the factor '(10 + t)' equal to zero and attempt to solve: Simplifying 10 + t = 0 Solving 10 + t = 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 + t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + t = 0 + -10 t = 0 + -10 Combine like terms: 0 + -10 = -10 t = -10 Simplifying t = -10Subproblem 4
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 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 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-10, 10, -10, 10}
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