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Simplifying 10d = 2d2 + 12 Reorder the terms: 10d = 12 + 2d2 Solving 10d = 12 + 2d2 Solving for variable 'd'. Reorder the terms: -12 + 10d + -2d2 = 12 + 2d2 + -12 + -2d2 Reorder the terms: -12 + 10d + -2d2 = 12 + -12 + 2d2 + -2d2 Combine like terms: 12 + -12 = 0 -12 + 10d + -2d2 = 0 + 2d2 + -2d2 -12 + 10d + -2d2 = 2d2 + -2d2 Combine like terms: 2d2 + -2d2 = 0 -12 + 10d + -2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 5d + -1d2) = 0 Factor a trinomial. 2((-3 + d)(2 + -1d)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + d)' equal to zero and attempt to solve: Simplifying -3 + d = 0 Solving -3 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + d = 0 + 3 Combine like terms: -3 + 3 = 0 0 + d = 0 + 3 d = 0 + 3 Combine like terms: 0 + 3 = 3 d = 3 Simplifying d = 3Subproblem 2
Set the factor '(2 + -1d)' equal to zero and attempt to solve: Simplifying 2 + -1d = 0 Solving 2 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1d = 0 + -2 -1d = 0 + -2 Combine like terms: 0 + -2 = -2 -1d = -2 Divide each side by '-1'. d = 2 Simplifying d = 2Solution
d = {3, 2}
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