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Simplifying t(4t + 1)(t + -2) = 0 Reorder the terms: t(1 + 4t)(t + -2) = 0 Reorder the terms: t(1 + 4t)(-2 + t) = 0 Multiply (1 + 4t) * (-2 + t) t(1(-2 + t) + 4t * (-2 + t)) = 0 t((-2 * 1 + t * 1) + 4t * (-2 + t)) = 0 t((-2 + 1t) + 4t * (-2 + t)) = 0 t(-2 + 1t + (-2 * 4t + t * 4t)) = 0 t(-2 + 1t + (-8t + 4t2)) = 0 Combine like terms: 1t + -8t = -7t t(-2 + -7t + 4t2) = 0 (-2 * t + -7t * t + 4t2 * t) = 0 (-2t + -7t2 + 4t3) = 0 Solving -2t + -7t2 + 4t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-2 + -7t + 4t2) = 0 Factor a trinomial. t((-1 + -4t)(2 + -1t)) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-1 + -4t)' equal to zero and attempt to solve: Simplifying -1 + -4t = 0 Solving -1 + -4t = 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 + -4t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4t = 0 + 1 -4t = 0 + 1 Combine like terms: 0 + 1 = 1 -4t = 1 Divide each side by '-4'. t = -0.25 Simplifying t = -0.25Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0, -0.25, 2}
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