(4m^2-6)(4m^2-6)=81

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Solution for (4m^2-6)(4m^2-6)=81 equation: 


Simplifying
(4m2 + -6)(4m2 + -6) = 81

Reorder the terms:
(-6 + 4m2)(4m2 + -6) = 81

Reorder the terms:
(-6 + 4m2)(-6 + 4m2) = 81

Multiply (-6 + 4m2) * (-6 + 4m2)
(-6(-6 + 4m2) + 4m2 * (-6 + 4m2)) = 81
((-6 * -6 + 4m2 * -6) + 4m2 * (-6 + 4m2)) = 81
((36 + -24m2) + 4m2 * (-6 + 4m2)) = 81
(36 + -24m2 + (-6 * 4m2 + 4m2 * 4m2)) = 81
(36 + -24m2 + (-24m2 + 16m4)) = 81

Combine like terms: -24m2 + -24m2 = -48m2
(36 + -48m2 + 16m4) = 81

Solving
36 + -48m2 + 16m4 = 81

Solving for variable 'm'.

Reorder the terms:
36 + -81 + -48m2 + 16m4 = 81 + -81

Combine like terms: 36 + -81 = -45
-45 + -48m2 + 16m4 = 81 + -81

Combine like terms: 81 + -81 = 0
-45 + -48m2 + 16m4 = 0

Factor a trinomial.
(-3 + -4m2)(15 + -4m2) = 0


Subproblem 1
Set the factor '(-3 + -4m2)' equal to zero and attempt to solve:

Simplifying
-3 + -4m2 = 0

Solving
-3 + -4m2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4m2 = 0 + 3
-4m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4m2 = 3

Divide each side by '-4'.
m2 = -0.75

Simplifying
m2 = -0.75

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(15 + -4m2)' equal to zero and attempt to solve:

Simplifying
15 + -4m2 = 0

Solving
15 + -4m2 = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4m2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4m2 = 0 + -15
-4m2 = 0 + -15

Combine like terms: 0 + -15 = -15
-4m2 = -15

Divide each side by '-4'.
m2 = 3.75

Simplifying
m2 = 3.75

Take the square root of each side:
m = {-1.936491673, 1.936491673}
Solution
m = {-1.936491673, 1.936491673}

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