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Simplifying 49t3 + 20t = -84t2 Reorder the terms: 20t + 49t3 = -84t2 Solving 20t + 49t3 = -84t2 Solving for variable 't'. Reorder the terms: 20t + 84t2 + 49t3 = -84t2 + 84t2 Combine like terms: -84t2 + 84t2 = 0 20t + 84t2 + 49t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(20 + 84t + 49t2) = 0 Factor a trinomial. t((10 + 7t)(2 + 7t)) = 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 '(10 + 7t)' equal to zero and attempt to solve: Simplifying 10 + 7t = 0 Solving 10 + 7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 7t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7t = 0 + -10 7t = 0 + -10 Combine like terms: 0 + -10 = -10 7t = -10 Divide each side by '7'. t = -1.428571429 Simplifying t = -1.428571429Subproblem 3
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 = -0.2857142857Solution
t = {0, -1.428571429, -0.2857142857}
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