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Simplifying (4t + 3)(t + -3) = 0 Reorder the terms: (3 + 4t)(t + -3) = 0 Reorder the terms: (3 + 4t)(-3 + t) = 0 Multiply (3 + 4t) * (-3 + t) (3(-3 + t) + 4t * (-3 + t)) = 0 ((-3 * 3 + t * 3) + 4t * (-3 + t)) = 0 ((-9 + 3t) + 4t * (-3 + t)) = 0 (-9 + 3t + (-3 * 4t + t * 4t)) = 0 (-9 + 3t + (-12t + 4t2)) = 0 Combine like terms: 3t + -12t = -9t (-9 + -9t + 4t2) = 0 Solving -9 + -9t + 4t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -4t)(3 + -1t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
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 = 3Solution
t = {-0.75, 3}
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