7d^2+32d-21=d-1

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Solution for 7d^2+32d-21=d-1 equation:


Simplifying
7d2 + 32d + -21 = d + -1

Reorder the terms:
-21 + 32d + 7d2 = d + -1

Reorder the terms:
-21 + 32d + 7d2 = -1 + d

Solving
-21 + 32d + 7d2 = -1 + d

Solving for variable 'd'.

Reorder the terms:
-21 + 1 + 32d + -1d + 7d2 = -1 + d + 1 + -1d

Combine like terms: -21 + 1 = -20
-20 + 32d + -1d + 7d2 = -1 + d + 1 + -1d

Combine like terms: 32d + -1d = 31d
-20 + 31d + 7d2 = -1 + d + 1 + -1d

Reorder the terms:
-20 + 31d + 7d2 = -1 + 1 + d + -1d

Combine like terms: -1 + 1 = 0
-20 + 31d + 7d2 = 0 + d + -1d
-20 + 31d + 7d2 = d + -1d

Combine like terms: d + -1d = 0
-20 + 31d + 7d2 = 0

Factor a trinomial.
(-5 + -1d)(4 + -7d) = 0

Subproblem 1

Set the factor '(-5 + -1d)' equal to zero and attempt to solve: Simplifying -5 + -1d = 0 Solving -5 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1d = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1d = 0 + 5 -1d = 0 + 5 Combine like terms: 0 + 5 = 5 -1d = 5 Divide each side by '-1'. d = -5 Simplifying d = -5

Subproblem 2

Set the factor '(4 + -7d)' equal to zero and attempt to solve: Simplifying 4 + -7d = 0 Solving 4 + -7d = 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 + -7d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7d = 0 + -4 -7d = 0 + -4 Combine like terms: 0 + -4 = -4 -7d = -4 Divide each side by '-7'. d = 0.5714285714 Simplifying d = 0.5714285714

Solution

d = {-5, 0.5714285714}

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