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Simplifying (7t + -2)(3t + -4) = 0 Reorder the terms: (-2 + 7t)(3t + -4) = 0 Reorder the terms: (-2 + 7t)(-4 + 3t) = 0 Multiply (-2 + 7t) * (-4 + 3t) (-2(-4 + 3t) + 7t * (-4 + 3t)) = 0 ((-4 * -2 + 3t * -2) + 7t * (-4 + 3t)) = 0 ((8 + -6t) + 7t * (-4 + 3t)) = 0 (8 + -6t + (-4 * 7t + 3t * 7t)) = 0 (8 + -6t + (-28t + 21t2)) = 0 Combine like terms: -6t + -28t = -34t (8 + -34t + 21t2) = 0 Solving 8 + -34t + 21t2 = 0 Solving for variable 't'. Factor a trinomial. (2 + -7t)(4 + -3t) = 0Subproblem 1
Set the factor '(2 + -7t)' equal to zero and attempt to solve: Simplifying 2 + -7t = 0 Solving 2 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7t = 0 + -2 -7t = 0 + -2 Combine like terms: 0 + -2 = -2 -7t = -2 Divide each side by '-7'. t = 0.2857142857 Simplifying t = 0.2857142857Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 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 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {0.2857142857, 1.333333333}
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