(5X^2-2)(3X^2-3)=

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

Simplifying
(5X2 + -2)(3X2 + -3) = 0

Reorder the terms:
(-2 + 5X2)(3X2 + -3) = 0

Reorder the terms:
(-2 + 5X2)(-3 + 3X2) = 0

Multiply (-2 + 5X2) * (-3 + 3X2)
(-2(-3 + 3X2) + 5X2 * (-3 + 3X2)) = 0
((-3 * -2 + 3X2 * -2) + 5X2 * (-3 + 3X2)) = 0
((6 + -6X2) + 5X2 * (-3 + 3X2)) = 0
(6 + -6X2 + (-3 * 5X2 + 3X2 * 5X2)) = 0
(6 + -6X2 + (-15X2 + 15X4)) = 0

Combine like terms: -6X2 + -15X2 = -21X2
(6 + -21X2 + 15X4) = 0

Solving
6 + -21X2 + 15X4 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -7X2 + 5X4) = 0

Factor a trinomial.
3((2 + -5X2)(1 + -1X2)) = 0

Factor a difference between two squares.
3((2 + -5X2)((1 + X)(1 + -1X))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -5X2)' equal to zero and attempt to solve:

Simplifying
2 + -5X2 = 0

Solving
2 + -5X2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5X2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5X2 = 0 + -2
-5X2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5X2 = -2

Divide each side by '-5'.
X2 = 0.4

Simplifying
X2 = 0.4

Take the square root of each side:
X = {-0.632455532, 0.632455532}
Subproblem 2
Set the factor '(1 + X)' equal to zero and attempt to solve:

Simplifying
1 + X = 0

Solving
1 + X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + X = 0 + -1
X = 0 + -1

Combine like terms: 0 + -1 = -1
X = -1

Simplifying
X = -1
Subproblem 3
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-0.632455532, 0.632455532, -1, 1}