(4x^2-6)(7x^2-7)=

Solution for (4x^2-6)(7x^2-7)= equation:

Simplifying
(4x2 + -6)(7x2 + -7) = 0

Reorder the terms:
(-6 + 4x2)(7x2 + -7) = 0

Reorder the terms:
(-6 + 4x2)(-7 + 7x2) = 0

Multiply (-6 + 4x2) * (-7 + 7x2)
(-6(-7 + 7x2) + 4x2 * (-7 + 7x2)) = 0
((-7 * -6 + 7x2 * -6) + 4x2 * (-7 + 7x2)) = 0
((42 + -42x2) + 4x2 * (-7 + 7x2)) = 0
(42 + -42x2 + (-7 * 4x2 + 7x2 * 4x2)) = 0
(42 + -42x2 + (-28x2 + 28x4)) = 0

Combine like terms: -42x2 + -28x2 = -70x2
(42 + -70x2 + 28x4) = 0

Solving
42 + -70x2 + 28x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(3 + -5x2 + 2x4) = 0

Factor a trinomial.
14((1 + -1x2)(3 + -2x2)) = 0

Factor a difference between two squares.
14(((1 + x)(1 + -1x))(3 + -2x2)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(3 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
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 = {-1.224744871, 1.224744871, -1, 1}