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Simplifying (4t + 1)(3t + -5) = 0 Reorder the terms: (1 + 4t)(3t + -5) = 0 Reorder the terms: (1 + 4t)(-5 + 3t) = 0 Multiply (1 + 4t) * (-5 + 3t) (1(-5 + 3t) + 4t * (-5 + 3t)) = 0 ((-5 * 1 + 3t * 1) + 4t * (-5 + 3t)) = 0 ((-5 + 3t) + 4t * (-5 + 3t)) = 0 (-5 + 3t + (-5 * 4t + 3t * 4t)) = 0 (-5 + 3t + (-20t + 12t2)) = 0 Combine like terms: 3t + -20t = -17t (-5 + -17t + 12t2) = 0 Solving -5 + -17t + 12t2 = 0 Solving for variable 't'. Factor a trinomial. (-1 + -4t)(5 + -3t) = 0Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve: Simplifying -1 + -4t = 0 Solving -1 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4t = 0 + 1 -4t = 0 + 1 Combine like terms: 0 + 1 = 1 -4t = 1 Divide each side by '-4'. t = -0.25 Simplifying t = -0.25Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 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 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {-0.25, 1.666666667}
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