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Simplifying (4t + -12)(5t + -25) = 0 Reorder the terms: (-12 + 4t)(5t + -25) = 0 Reorder the terms: (-12 + 4t)(-25 + 5t) = 0 Multiply (-12 + 4t) * (-25 + 5t) (-12(-25 + 5t) + 4t * (-25 + 5t)) = 0 ((-25 * -12 + 5t * -12) + 4t * (-25 + 5t)) = 0 ((300 + -60t) + 4t * (-25 + 5t)) = 0 (300 + -60t + (-25 * 4t + 5t * 4t)) = 0 (300 + -60t + (-100t + 20t2)) = 0 Combine like terms: -60t + -100t = -160t (300 + -160t + 20t2) = 0 Solving 300 + -160t + 20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '20'. 20(15 + -8t + t2) = 0 Factor a trinomial. 20((3 + -1t)(5 + -1t)) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 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 = 5Solution
t = {3, 5}
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