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Simplifying (7t + 4)(3t + -5) = 0 Reorder the terms: (4 + 7t)(3t + -5) = 0 Reorder the terms: (4 + 7t)(-5 + 3t) = 0 Multiply (4 + 7t) * (-5 + 3t) (4(-5 + 3t) + 7t * (-5 + 3t)) = 0 ((-5 * 4 + 3t * 4) + 7t * (-5 + 3t)) = 0 ((-20 + 12t) + 7t * (-5 + 3t)) = 0 (-20 + 12t + (-5 * 7t + 3t * 7t)) = 0 (-20 + 12t + (-35t + 21t2)) = 0 Combine like terms: 12t + -35t = -23t (-20 + -23t + 21t2) = 0 Solving -20 + -23t + 21t2 = 0 Solving for variable 't'. Factor a trinomial. (-4 + -7t)(5 + -3t) = 0Subproblem 1
Set the factor '(-4 + -7t)' equal to zero and attempt to solve: Simplifying -4 + -7t = 0 Solving -4 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7t = 0 + 4 -7t = 0 + 4 Combine like terms: 0 + 4 = 4 -7t = 4 Divide each side by '-7'. t = -0.5714285714 Simplifying t = -0.5714285714Subproblem 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 = {-0.5714285714, 1.666666667}
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