14d^2+77d+84=0

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Solution for 14d^2+77d+84=0 equation:


Simplifying
14d2 + 77d + 84 = 0

Reorder the terms:
84 + 77d + 14d2 = 0

Solving
84 + 77d + 14d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + 11d + 2d2) = 0

Factor a trinomial.
7((4 + d)(3 + 2d)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(4 + d)' equal to zero and attempt to solve: Simplifying 4 + d = 0 Solving 4 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + d = 0 + -4 d = 0 + -4 Combine like terms: 0 + -4 = -4 d = -4 Simplifying d = -4

Subproblem 2

Set the factor '(3 + 2d)' equal to zero and attempt to solve: Simplifying 3 + 2d = 0 Solving 3 + 2d = 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 + 2d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2d = 0 + -3 2d = 0 + -3 Combine like terms: 0 + -3 = -3 2d = -3 Divide each side by '2'. d = -1.5 Simplifying d = -1.5

Solution

d = {-4, -1.5}

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