(x^2-4)(x^2-9)=7x^2

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Solution for (x^2-4)(x^2-9)=7x^2 equation: 


Simplifying
(x2 + -4)(x2 + -9) = 7x2

Reorder the terms:
(-4 + x2)(x2 + -9) = 7x2

Reorder the terms:
(-4 + x2)(-9 + x2) = 7x2

Multiply (-4 + x2) * (-9 + x2)
(-4(-9 + x2) + x2(-9 + x2)) = 7x2
((-9 * -4 + x2 * -4) + x2(-9 + x2)) = 7x2
((36 + -4x2) + x2(-9 + x2)) = 7x2
(36 + -4x2 + (-9 * x2 + x2 * x2)) = 7x2
(36 + -4x2 + (-9x2 + x4)) = 7x2

Combine like terms: -4x2 + -9x2 = -13x2
(36 + -13x2 + x4) = 7x2

Solving
36 + -13x2 + x4 = 7x2

Solving for variable 'x'.

Reorder the terms:
36 + -13x2 + -7x2 + x4 = 7x2 + -7x2

Combine like terms: -13x2 + -7x2 = -20x2
36 + -20x2 + x4 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
36 + -20x2 + x4 = 0

Factor a trinomial.
(2 + -1x2)(18 + -1x2) = 0


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

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(18 + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -1x2 = 0

Solving
18 + -1x2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x2 = 0 + -18
-1x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1x2 = -18

Divide each side by '-1'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}
Solution
x = {-1.414213562, 1.414213562, -4.242640687, 4.242640687}

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