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Simplifying (3t + -2)(4t + 2) = 0 Reorder the terms: (-2 + 3t)(4t + 2) = 0 Reorder the terms: (-2 + 3t)(2 + 4t) = 0 Multiply (-2 + 3t) * (2 + 4t) (-2(2 + 4t) + 3t * (2 + 4t)) = 0 ((2 * -2 + 4t * -2) + 3t * (2 + 4t)) = 0 ((-4 + -8t) + 3t * (2 + 4t)) = 0 (-4 + -8t + (2 * 3t + 4t * 3t)) = 0 (-4 + -8t + (6t + 12t2)) = 0 Combine like terms: -8t + 6t = -2t (-4 + -2t + 12t2) = 0 Solving -4 + -2t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -1t + 6t2) = 0 Factor a trinomial. 2((-1 + -2t)(2 + -3t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve: Simplifying 2 + -3t = 0 Solving 2 + -3t = 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 + -3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3t = 0 + -2 -3t = 0 + -2 Combine like terms: 0 + -2 = -2 -3t = -2 Divide each side by '-3'. t = 0.6666666667 Simplifying t = 0.6666666667Solution
t = {-0.5, 0.6666666667}
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