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Simplifying 7t(t + -4) + -2t(8t + -4t + 3) = 0 Reorder the terms: 7t(-4 + t) + -2t(8t + -4t + 3) = 0 (-4 * 7t + t * 7t) + -2t(8t + -4t + 3) = 0 (-28t + 7t2) + -2t(8t + -4t + 3) = 0 Reorder the terms: -28t + 7t2 + -2t(3 + 8t + -4t) = 0 Combine like terms: 8t + -4t = 4t -28t + 7t2 + -2t(3 + 4t) = 0 -28t + 7t2 + (3 * -2t + 4t * -2t) = 0 -28t + 7t2 + (-6t + -8t2) = 0 Reorder the terms: -28t + -6t + 7t2 + -8t2 = 0 Combine like terms: -28t + -6t = -34t -34t + 7t2 + -8t2 = 0 Combine like terms: 7t2 + -8t2 = -1t2 -34t + -1t2 = 0 Solving -34t + -1t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1t'. -1t(34 + t) = 0 Ignore the factor -1.Subproblem 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 '(34 + t)' equal to zero and attempt to solve: Simplifying 34 + t = 0 Solving 34 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + t = 0 + -34 Combine like terms: 34 + -34 = 0 0 + t = 0 + -34 t = 0 + -34 Combine like terms: 0 + -34 = -34 t = -34 Simplifying t = -34Solution
t = {0, -34}
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