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Simplifying (t2 + 8t + 16)[(t + 4) + -4] = 0 Reorder the terms: (16 + 8t + t2)[(t + 4) + -4] = 0 Reorder the terms: (16 + 8t + t2)[(4 + t) + -4] = 0 Remove parenthesis around (4 + t) (16 + 8t + t2)[4 + t + -4] = 0 Reorder the terms: (16 + 8t + t2)[4 + -4 + t] = 0 Combine like terms: 4 + -4 = 0 (16 + 8t + t2)[0 + t] = 0 (16 + 8t + t2)[t] = 0 Reorder the terms for easier multiplication: t(16 + 8t + t2) = 0 (16 * t + 8t * t + t2 * t) = 0 (16t + 8t2 + t3) = 0 Solving 16t + 8t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(16 + 8t + t2) = 0 Factor a trinomial. t((4 + t)(4 + t)) = 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 '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Subproblem 3
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Solution
t = {0, -4, -4}
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