x^2(x^2-49)-64(x^2-49)=0

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Solution for x^2(x^2-49)-64(x^2-49)=0 equation: 


Simplifying
x2(x2 + -49) + -64(x2 + -49) = 0

Reorder the terms:
x2(-49 + x2) + -64(x2 + -49) = 0
(-49 * x2 + x2 * x2) + -64(x2 + -49) = 0
(-49x2 + x4) + -64(x2 + -49) = 0

Reorder the terms:
-49x2 + x4 + -64(-49 + x2) = 0
-49x2 + x4 + (-49 * -64 + x2 * -64) = 0
-49x2 + x4 + (3136 + -64x2) = 0

Reorder the terms:
3136 + -49x2 + -64x2 + x4 = 0

Combine like terms: -49x2 + -64x2 = -113x2
3136 + -113x2 + x4 = 0

Solving
3136 + -113x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(49 + -1x2)(64 + -1x2) = 0

Factor a difference between two squares.
((7 + x)(7 + -1x))(64 + -1x2) = 0

Factor a difference between two squares.
((8 + x)(8 + -1x))(7 + x)(7 + -1x) = 0


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

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

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

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

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

Simplifying
x = 7

Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 4
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-7, 7, -8, 8}

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