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Simplifying 4r2 + 12rt + 9t2 = 0 Reorder the terms: 12rt + 4r2 + 9t2 = 0 Solving 12rt + 4r2 + 9t2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + 3t)(2r + 3t) = 0Subproblem 1
Set the factor '(2r + 3t)' equal to zero and attempt to solve: Simplifying 2r + 3t = 0 Solving 2r + 3t = 0 Move all terms containing r to the left, all other terms to the right. Add '-3t' to each side of the equation. 2r + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 2r + 0 = 0 + -3t 2r = 0 + -3t Remove the zero: 2r = -3t Divide each side by '2'. r = -1.5t Simplifying r = -1.5tSubproblem 2
Set the factor '(2r + 3t)' equal to zero and attempt to solve: Simplifying 2r + 3t = 0 Solving 2r + 3t = 0 Move all terms containing r to the left, all other terms to the right. Add '-3t' to each side of the equation. 2r + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 2r + 0 = 0 + -3t 2r = 0 + -3t Remove the zero: 2r = -3t Divide each side by '2'. r = -1.5t Simplifying r = -1.5tSolution
r = {-1.5t, -1.5t}
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