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Simplifying (7t + 4)(3t + -8) = 0 Reorder the terms: (4 + 7t)(3t + -8) = 0 Reorder the terms: (4 + 7t)(-8 + 3t) = 0 Multiply (4 + 7t) * (-8 + 3t) (4(-8 + 3t) + 7t * (-8 + 3t)) = 0 ((-8 * 4 + 3t * 4) + 7t * (-8 + 3t)) = 0 ((-32 + 12t) + 7t * (-8 + 3t)) = 0 (-32 + 12t + (-8 * 7t + 3t * 7t)) = 0 (-32 + 12t + (-56t + 21t2)) = 0 Combine like terms: 12t + -56t = -44t (-32 + -44t + 21t2) = 0 Solving -32 + -44t + 21t2 = 0 Solving for variable 't'. Factor a trinomial. (-4 + -7t)(8 + -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 '(8 + -3t)' equal to zero and attempt to solve: Simplifying 8 + -3t = 0 Solving 8 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3t = 0 + -8 -3t = 0 + -8 Combine like terms: 0 + -8 = -8 -3t = -8 Divide each side by '-3'. t = 2.666666667 Simplifying t = 2.666666667Solution
t = {-0.5714285714, 2.666666667}
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