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Simplifying (5t + -3)(2t + -4) = 0 Reorder the terms: (-3 + 5t)(2t + -4) = 0 Reorder the terms: (-3 + 5t)(-4 + 2t) = 0 Multiply (-3 + 5t) * (-4 + 2t) (-3(-4 + 2t) + 5t * (-4 + 2t)) = 0 ((-4 * -3 + 2t * -3) + 5t * (-4 + 2t)) = 0 ((12 + -6t) + 5t * (-4 + 2t)) = 0 (12 + -6t + (-4 * 5t + 2t * 5t)) = 0 (12 + -6t + (-20t + 10t2)) = 0 Combine like terms: -6t + -20t = -26t (12 + -26t + 10t2) = 0 Solving 12 + -26t + 10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -13t + 5t2) = 0 Factor a trinomial. 2((3 + -5t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -5t)' equal to zero and attempt to solve: Simplifying 3 + -5t = 0 Solving 3 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5t = 0 + -3 -5t = 0 + -3 Combine like terms: 0 + -3 = -3 -5t = -3 Divide each side by '-5'. t = 0.6 Simplifying t = 0.6Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0.6, 2}
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