7(d-2)=5d(d+2)

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Solution for 7(d-2)=5d(d+2) equation:


Simplifying
7(d + -2) = 5d(d + 2)

Reorder the terms:
7(-2 + d) = 5d(d + 2)
(-2 * 7 + d * 7) = 5d(d + 2)
(-14 + 7d) = 5d(d + 2)

Reorder the terms:
-14 + 7d = 5d(2 + d)
-14 + 7d = (2 * 5d + d * 5d)
-14 + 7d = (10d + 5d2)

Solving
-14 + 7d = 10d + 5d2

Solving for variable 'd'.

Combine like terms: 7d + -10d = -3d
-14 + -3d + -5d2 = 10d + 5d2 + -10d + -5d2

Reorder the terms:
-14 + -3d + -5d2 = 10d + -10d + 5d2 + -5d2

Combine like terms: 10d + -10d = 0
-14 + -3d + -5d2 = 0 + 5d2 + -5d2
-14 + -3d + -5d2 = 5d2 + -5d2

Combine like terms: 5d2 + -5d2 = 0
-14 + -3d + -5d2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 3d + 5d2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(14 + 3d + 5d2)' equal to zero and attempt to solve: Simplifying 14 + 3d + 5d2 = 0 Solving 14 + 3d + 5d2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 0.6d + d2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 0.6d + -2.8 + d2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 0.6d + d2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 0.6d + d2 = 0 + -2.8 0.6d + d2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 0.6d + d2 = -2.8 The d term is 0.6d. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6d + 0.09 + d2 = -2.8 + 0.09 Reorder the terms: 0.09 + 0.6d + d2 = -2.8 + 0.09 Combine like terms: -2.8 + 0.09 = -2.71 0.09 + 0.6d + d2 = -2.71 Factor a perfect square on the left side: (d + 0.3)(d + 0.3) = -2.71 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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