(5x^2+1)(2x^2-7)=

Solution for (5x^2+1)(2x^2-7)= equation:

Simplifying
(5x2 + 1)(2x2 + -7) = 0

Reorder the terms:
(1 + 5x2)(2x2 + -7) = 0

Reorder the terms:
(1 + 5x2)(-7 + 2x2) = 0

Multiply (1 + 5x2) * (-7 + 2x2)
(1(-7 + 2x2) + 5x2 * (-7 + 2x2)) = 0
((-7 * 1 + 2x2 * 1) + 5x2 * (-7 + 2x2)) = 0
((-7 + 2x2) + 5x2 * (-7 + 2x2)) = 0
(-7 + 2x2 + (-7 * 5x2 + 2x2 * 5x2)) = 0
(-7 + 2x2 + (-35x2 + 10x4)) = 0

Combine like terms: 2x2 + -35x2 = -33x2
(-7 + -33x2 + 10x4) = 0

Solving
-7 + -33x2 + 10x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -5x2)(7 + -2x2) = 0

Subproblem 1
Set the factor '(-1 + -5x2)' equal to zero and attempt to solve:

Simplifying
-1 + -5x2 = 0

Solving
-1 + -5x2 = 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 + -5x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x2 = 0 + 1
-5x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5x2 = 1

Divide each side by '-5'.
x2 = -0.2

Simplifying
x2 = -0.2

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 '(7 + -2x2)' equal to zero and attempt to solve:

Simplifying
7 + -2x2 = 0

Solving
7 + -2x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x2 = 0 + -7
-2x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-2x2 = -7

Divide each side by '-2'.
x2 = 3.5

Simplifying
x2 = 3.5

Take the square root of each side:
x = {-1.870828693, 1.870828693}
Solution
x = {-1.870828693, 1.870828693}