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Simplifying (5t2 + -13t)(t + 5) = 0 Reorder the terms: (-13t + 5t2)(t + 5) = 0 Reorder the terms: (-13t + 5t2)(5 + t) = 0 Multiply (-13t + 5t2) * (5 + t) (-13t * (5 + t) + 5t2 * (5 + t)) = 0 ((5 * -13t + t * -13t) + 5t2 * (5 + t)) = 0 ((-65t + -13t2) + 5t2 * (5 + t)) = 0 (-65t + -13t2 + (5 * 5t2 + t * 5t2)) = 0 (-65t + -13t2 + (25t2 + 5t3)) = 0 Combine like terms: -13t2 + 25t2 = 12t2 (-65t + 12t2 + 5t3) = 0 Solving -65t + 12t2 + 5t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-65 + 12t + 5t2) = 0 Factor a trinomial. t((-5 + -1t)(13 + -5t)) = 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 '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 3
Set the factor '(13 + -5t)' equal to zero and attempt to solve: Simplifying 13 + -5t = 0 Solving 13 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -5t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -5t = 0 + -13 -5t = 0 + -13 Combine like terms: 0 + -13 = -13 -5t = -13 Divide each side by '-5'. t = 2.6 Simplifying t = 2.6Solution
t = {0, -5, 2.6}
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