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Simplifying (2t + 8)(4t + -2) = 0 Reorder the terms: (8 + 2t)(4t + -2) = 0 Reorder the terms: (8 + 2t)(-2 + 4t) = 0 Multiply (8 + 2t) * (-2 + 4t) (8(-2 + 4t) + 2t * (-2 + 4t)) = 0 ((-2 * 8 + 4t * 8) + 2t * (-2 + 4t)) = 0 ((-16 + 32t) + 2t * (-2 + 4t)) = 0 (-16 + 32t + (-2 * 2t + 4t * 2t)) = 0 (-16 + 32t + (-4t + 8t2)) = 0 Combine like terms: 32t + -4t = 28t (-16 + 28t + 8t2) = 0 Solving -16 + 28t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 7t + 2t2) = 0 Factor a trinomial. 4((-4 + -1t)(1 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 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 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Solution
t = {-4, 0.5}
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