(5x^2-8)(x^2-7)=0

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Solution for (5x^2-8)(x^2-7)=0 equation: 


Simplifying
(5x2 + -8)(x2 + -7) = 0

Reorder the terms:
(-8 + 5x2)(x2 + -7) = 0

Reorder the terms:
(-8 + 5x2)(-7 + x2) = 0

Multiply (-8 + 5x2) * (-7 + x2)
(-8(-7 + x2) + 5x2 * (-7 + x2)) = 0
((-7 * -8 + x2 * -8) + 5x2 * (-7 + x2)) = 0
((56 + -8x2) + 5x2 * (-7 + x2)) = 0
(56 + -8x2 + (-7 * 5x2 + x2 * 5x2)) = 0
(56 + -8x2 + (-35x2 + 5x4)) = 0

Combine like terms: -8x2 + -35x2 = -43x2
(56 + -43x2 + 5x4) = 0

Solving
56 + -43x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -5x2)(7 + -1x2) = 0


Subproblem 1
Set the factor '(8 + -5x2)' equal to zero and attempt to solve:

Simplifying
8 + -5x2 = 0

Solving
8 + -5x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x2 = 0 + -8
-5x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-5x2 = -8

Divide each side by '-5'.
x2 = 1.6

Simplifying
x2 = 1.6

Take the square root of each side:
x = {-1.264911064, 1.264911064}

Subproblem 2
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 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 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {-1.264911064, 1.264911064, -2.645751311, 2.645751311}

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