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Simplifying 3t3 + -12t = 135t Reorder the terms: -12t + 3t3 = 135t Solving -12t + 3t3 = 135t Solving for variable 't'. Reorder the terms: -12t + -135t + 3t3 = 135t + -135t Combine like terms: -12t + -135t = -147t -147t + 3t3 = 135t + -135t Combine like terms: 135t + -135t = 0 -147t + 3t3 = 0 Factor out the Greatest Common Factor (GCF), '3t'. 3t(-49 + t2) = 0 Factor a difference between two squares. 3t((7 + t)(-7 + t)) = 0 Ignore the factor 3.Subproblem 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 '(7 + t)' equal to zero and attempt to solve: Simplifying 7 + t = 0 Solving 7 + t = 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 + t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + t = 0 + -7 t = 0 + -7 Combine like terms: 0 + -7 = -7 t = -7 Simplifying t = -7Subproblem 3
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 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 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Solution
t = {0, -7, 7}
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