(5s^2-4d^2)(5s^2-4d^2)=

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Solution for (5s^2-4d^2)(5s^2-4d^2)= equation: 


Simplifying
(5s2 + -4d2)(5s2 + -4d2) = 0

Reorder the terms:
(-4d2 + 5s2)(5s2 + -4d2) = 0

Reorder the terms:
(-4d2 + 5s2)(-4d2 + 5s2) = 0

Multiply (-4d2 + 5s2) * (-4d2 + 5s2)
(-4d2 * (-4d2 + 5s2) + 5s2 * (-4d2 + 5s2)) = 0
((-4d2 * -4d2 + 5s2 * -4d2) + 5s2 * (-4d2 + 5s2)) = 0

Reorder the terms:
((-20d2s2 + 16d4) + 5s2 * (-4d2 + 5s2)) = 0
((-20d2s2 + 16d4) + 5s2 * (-4d2 + 5s2)) = 0
(-20d2s2 + 16d4 + (-4d2 * 5s2 + 5s2 * 5s2)) = 0
(-20d2s2 + 16d4 + (-20d2s2 + 25s4)) = 0

Reorder the terms:
(-20d2s2 + -20d2s2 + 16d4 + 25s4) = 0

Combine like terms: -20d2s2 + -20d2s2 = -40d2s2
(-40d2s2 + 16d4 + 25s4) = 0

Solving
-40d2s2 + 16d4 + 25s4 = 0

Solving for variable 'd'.

Factor a trinomial.
(4d2 + -5s2)(4d2 + -5s2) = 0


Subproblem 1
Set the factor '(4d2 + -5s2)' equal to zero and attempt to solve:

Simplifying
4d2 + -5s2 = 0

Solving
4d2 + -5s2 = 0

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

Add '5s2' to each side of the equation.
4d2 + -5s2 + 5s2 = 0 + 5s2

Combine like terms: -5s2 + 5s2 = 0
4d2 + 0 = 0 + 5s2
4d2 = 0 + 5s2
Remove the zero:
4d2 = 5s2

Divide each side by '4'.
d2 = 1.25s2

Simplifying
d2 = 1.25s2

Take the square root of each side:
d = {-1.118033989s, 1.118033989s}

Subproblem 2
Set the factor '(4d2 + -5s2)' equal to zero and attempt to solve:

Simplifying
4d2 + -5s2 = 0

Solving
4d2 + -5s2 = 0

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

Add '5s2' to each side of the equation.
4d2 + -5s2 + 5s2 = 0 + 5s2

Combine like terms: -5s2 + 5s2 = 0
4d2 + 0 = 0 + 5s2
4d2 = 0 + 5s2
Remove the zero:
4d2 = 5s2

Divide each side by '4'.
d2 = 1.25s2

Simplifying
d2 = 1.25s2

Take the square root of each side:
d = {-1.118033989s, 1.118033989s}
Solution
d = {-1.118033989s, 1.118033989s, -1.118033989s, 1.118033989s}

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