-2d(4d^2+3d-2)=

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Solution for -2d(4d^2+3d-2)= equation:


Simplifying
-2d(4d2 + 3d + -2) = 0

Reorder the terms:
-2d(-2 + 3d + 4d2) = 0
(-2 * -2d + 3d * -2d + 4d2 * -2d) = 0
(4d + -6d2 + -8d3) = 0

Solving
4d + -6d2 + -8d3 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2d'.
2d(2 + -3d + -4d2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0

Subproblem 2

Set the factor '(2 + -3d + -4d2)' equal to zero and attempt to solve: Simplifying 2 + -3d + -4d2 = 0 Solving 2 + -3d + -4d2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 0.75d + d2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.75d + 0.5 + d2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.75d + d2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.75d + d2 = 0 + 0.5 0.75d + d2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.75d + d2 = 0.5 The d term is 0.75d. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75d + 0.140625 + d2 = 0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75d + d2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + 0.75d + d2 = 0.640625 Factor a perfect square on the left side: (d + 0.375)(d + 0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (d + 0.375) equal to 0.80039053 and -0.80039053.

Subproblem 1

d + 0.375 = 0.80039053 Simplifying d + 0.375 = 0.80039053 Reorder the terms: 0.375 + d = 0.80039053 Solving 0.375 + d = 0.80039053 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + d = 0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + d = 0.80039053 + -0.375 d = 0.80039053 + -0.375 Combine like terms: 0.80039053 + -0.375 = 0.42539053 d = 0.42539053 Simplifying d = 0.42539053

Subproblem 2

d + 0.375 = -0.80039053 Simplifying d + 0.375 = -0.80039053 Reorder the terms: 0.375 + d = -0.80039053 Solving 0.375 + d = -0.80039053 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + d = -0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + d = -0.80039053 + -0.375 d = -0.80039053 + -0.375 Combine like terms: -0.80039053 + -0.375 = -1.17539053 d = -1.17539053 Simplifying d = -1.17539053

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.42539053, -1.17539053}

Solution

d = {0, 0.42539053, -1.17539053}

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