(a^2-3d^2)(a^2-5d^2)=

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Solution for (a^2-3d^2)(a^2-5d^2)= equation: 


Simplifying
(a2 + -3d2)(a2 + -5d2) = 0

Multiply (a2 + -3d2) * (a2 + -5d2)
(a2(a2 + -5d2) + -3d2 * (a2 + -5d2)) = 0
((a2 * a2 + -5d2 * a2) + -3d2 * (a2 + -5d2)) = 0

Reorder the terms:
((-5a2d2 + a4) + -3d2 * (a2 + -5d2)) = 0
((-5a2d2 + a4) + -3d2 * (a2 + -5d2)) = 0
(-5a2d2 + a4 + (a2 * -3d2 + -5d2 * -3d2)) = 0
(-5a2d2 + a4 + (-3a2d2 + 15d4)) = 0

Reorder the terms:
(-5a2d2 + -3a2d2 + a4 + 15d4) = 0

Combine like terms: -5a2d2 + -3a2d2 = -8a2d2
(-8a2d2 + a4 + 15d4) = 0

Solving
-8a2d2 + a4 + 15d4 = 0

Solving for variable 'a'.

Factor a trinomial.
(a2 + -5d2)(a2 + -3d2) = 0


Subproblem 1
Set the factor '(a2 + -5d2)' equal to zero and attempt to solve:

Simplifying
a2 + -5d2 = 0

Solving
a2 + -5d2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '5d2' to each side of the equation.
a2 + -5d2 + 5d2 = 0 + 5d2

Combine like terms: -5d2 + 5d2 = 0
a2 + 0 = 0 + 5d2
a2 = 0 + 5d2
Remove the zero:
a2 = 5d2

Simplifying
a2 = 5d2

Take the square root of each side:
a = {-2.236067978d, 2.236067978d}

Subproblem 2
Set the factor '(a2 + -3d2)' equal to zero and attempt to solve:

Simplifying
a2 + -3d2 = 0

Solving
a2 + -3d2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '3d2' to each side of the equation.
a2 + -3d2 + 3d2 = 0 + 3d2

Combine like terms: -3d2 + 3d2 = 0
a2 + 0 = 0 + 3d2
a2 = 0 + 3d2
Remove the zero:
a2 = 3d2

Simplifying
a2 = 3d2

Take the square root of each side:
a = {-1.732050808d, 1.732050808d}
Solution
a = {-2.236067978d, 2.236067978d, -1.732050808d, 1.732050808d}

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