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Simplifying (5t + 2)(2t + -7) = 0 Reorder the terms: (2 + 5t)(2t + -7) = 0 Reorder the terms: (2 + 5t)(-7 + 2t) = 0 Multiply (2 + 5t) * (-7 + 2t) (2(-7 + 2t) + 5t * (-7 + 2t)) = 0 ((-7 * 2 + 2t * 2) + 5t * (-7 + 2t)) = 0 ((-14 + 4t) + 5t * (-7 + 2t)) = 0 (-14 + 4t + (-7 * 5t + 2t * 5t)) = 0 (-14 + 4t + (-35t + 10t2)) = 0 Combine like terms: 4t + -35t = -31t (-14 + -31t + 10t2) = 0 Solving -14 + -31t + 10t2 = 0 Solving for variable 't'. Factor a trinomial. (-2 + -5t)(7 + -2t) = 0Subproblem 1
Set the factor '(-2 + -5t)' equal to zero and attempt to solve: Simplifying -2 + -5t = 0 Solving -2 + -5t = 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 + -5t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5t = 0 + 2 -5t = 0 + 2 Combine like terms: 0 + 2 = 2 -5t = 2 Divide each side by '-5'. t = -0.4 Simplifying t = -0.4Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {-0.4, 3.5}
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