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Simplifying (3t + -2)(4t + 5) = 0 Reorder the terms: (-2 + 3t)(4t + 5) = 0 Reorder the terms: (-2 + 3t)(5 + 4t) = 0 Multiply (-2 + 3t) * (5 + 4t) (-2(5 + 4t) + 3t * (5 + 4t)) = 0 ((5 * -2 + 4t * -2) + 3t * (5 + 4t)) = 0 ((-10 + -8t) + 3t * (5 + 4t)) = 0 (-10 + -8t + (5 * 3t + 4t * 3t)) = 0 (-10 + -8t + (15t + 12t2)) = 0 Combine like terms: -8t + 15t = 7t (-10 + 7t + 12t2) = 0 Solving -10 + 7t + 12t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -4t)(2 + -3t) = 0Subproblem 1
Set the factor '(-5 + -4t)' equal to zero and attempt to solve: Simplifying -5 + -4t = 0 Solving -5 + -4t = 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 + -4t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4t = 0 + 5 -4t = 0 + 5 Combine like terms: 0 + 5 = 5 -4t = 5 Divide each side by '-4'. t = -1.25 Simplifying t = -1.25Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve: Simplifying 2 + -3t = 0 Solving 2 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3t = 0 + -2 -3t = 0 + -2 Combine like terms: 0 + -2 = -2 -3t = -2 Divide each side by '-3'. t = 0.6666666667 Simplifying t = 0.6666666667Solution
t = {-1.25, 0.6666666667}
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