(2m^2+5)(3m^2-6)=

Solution for (2m^2+5)(3m^2-6)= equation:

Simplifying
(2m2 + 5)(3m2 + -6) = 0

Reorder the terms:
(5 + 2m2)(3m2 + -6) = 0

Reorder the terms:
(5 + 2m2)(-6 + 3m2) = 0

Multiply (5 + 2m2) * (-6 + 3m2)
(5(-6 + 3m2) + 2m2 * (-6 + 3m2)) = 0
((-6 * 5 + 3m2 * 5) + 2m2 * (-6 + 3m2)) = 0
((-30 + 15m2) + 2m2 * (-6 + 3m2)) = 0
(-30 + 15m2 + (-6 * 2m2 + 3m2 * 2m2)) = 0
(-30 + 15m2 + (-12m2 + 6m4)) = 0

Combine like terms: 15m2 + -12m2 = 3m2
(-30 + 3m2 + 6m4) = 0

Solving
-30 + 3m2 + 6m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + m2 + 2m4) = 0

Factor a trinomial.
3((-5 + -2m2)(2 + -1m2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2m2)' equal to zero and attempt to solve:

Simplifying
-5 + -2m2 = 0

Solving
-5 + -2m2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2m2 = 0 + 5
-2m2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2m2 = 5

Divide each side by '-2'.
m2 = -2.5

Simplifying
m2 = -2.5

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 '(2 + -1m2)' equal to zero and attempt to solve:

Simplifying
2 + -1m2 = 0

Solving
2 + -1m2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m2 = 0 + -2
-1m2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1m2 = -2

Divide each side by '-1'.
m2 = 2

Simplifying
m2 = 2

Take the square root of each side:
m = {-1.414213562, 1.414213562}
Solution
m = {-1.414213562, 1.414213562}