(7y^2-2)(2y^2-1)=

Solution for (7y^2-2)(2y^2-1)= equation:

Simplifying
(7y2 + -2)(2y2 + -1) = 0

Reorder the terms:
(-2 + 7y2)(2y2 + -1) = 0

Reorder the terms:
(-2 + 7y2)(-1 + 2y2) = 0

Multiply (-2 + 7y2) * (-1 + 2y2)
(-2(-1 + 2y2) + 7y2 * (-1 + 2y2)) = 0
((-1 * -2 + 2y2 * -2) + 7y2 * (-1 + 2y2)) = 0
((2 + -4y2) + 7y2 * (-1 + 2y2)) = 0
(2 + -4y2 + (-1 * 7y2 + 2y2 * 7y2)) = 0
(2 + -4y2 + (-7y2 + 14y4)) = 0

Combine like terms: -4y2 + -7y2 = -11y2
(2 + -11y2 + 14y4) = 0

Solving
2 + -11y2 + 14y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + -7y2)(1 + -2y2) = 0

Subproblem 1
Set the factor '(2 + -7y2)' equal to zero and attempt to solve:

Simplifying
2 + -7y2 = 0

Solving
2 + -7y2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7y2 = 0 + -2
-7y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7y2 = -2

Divide each side by '-7'.
y2 = 0.2857142857

Simplifying
y2 = 0.2857142857

Take the square root of each side:
y = {-0.534522484, 0.534522484}
Subproblem 2
Set the factor '(1 + -2y2)' equal to zero and attempt to solve:

Simplifying
1 + -2y2 = 0

Solving
1 + -2y2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y2 = 0 + -1
-2y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2y2 = -1

Divide each side by '-2'.
y2 = 0.5

Simplifying
y2 = 0.5

Take the square root of each side:
y = {-0.707106781, 0.707106781}
Solution
y = {-0.534522484, 0.534522484, -0.707106781, 0.707106781}