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Simplifying 6x2 + dx + -12d2 = 0 Reorder the terms: dx + -12d2 + 6x2 = 0 Solving dx + -12d2 + 6x2 = 0 Solving for variable 'd'. Factor a trinomial. (-3d + -2x)(4d + -3x) = 0Subproblem 1
Set the factor '(-3d + -2x)' equal to zero and attempt to solve: Simplifying -3d + -2x = 0 Solving -3d + -2x = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -3d + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 -3d + 0 = 0 + 2x -3d = 0 + 2x Remove the zero: -3d = 2x Divide each side by '-3'. d = -0.6666666667x Simplifying d = -0.6666666667xSubproblem 2
Set the factor '(4d + -3x)' equal to zero and attempt to solve: Simplifying 4d + -3x = 0 Solving 4d + -3x = 0 Move all terms containing d to the left, all other terms to the right. Add '3x' to each side of the equation. 4d + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 4d + 0 = 0 + 3x 4d = 0 + 3x Remove the zero: 4d = 3x Divide each side by '4'. d = 0.75x Simplifying d = 0.75xSolution
d = {-0.6666666667x, 0.75x}
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