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Simplifying t(2t + 6) = 56 Reorder the terms: t(6 + 2t) = 56 (6 * t + 2t * t) = 56 (6t + 2t2) = 56 Solving 6t + 2t2 = 56 Solving for variable 't'. Reorder the terms: -56 + 6t + 2t2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 6t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 3t + t2) = 0 Factor a trinomial. 2((-7 + -1t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve: Simplifying -7 + -1t = 0 Solving -7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t = 0 + 7 -1t = 0 + 7 Combine like terms: 0 + 7 = 7 -1t = 7 Divide each side by '-1'. t = -7 Simplifying t = -7Subproblem 2
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 = 4Solution
t = {-7, 4}
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