36x^4-148x^2=-16

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Solution for 36x^4-148x^2=-16 equation: 


Simplifying
36x4 + -148x2 = -16

Reorder the terms:
-148x2 + 36x4 = -16

Solving
-148x2 + 36x4 = -16

Solving for variable 'x'.

Reorder the terms:
16 + -148x2 + 36x4 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -148x2 + 36x4 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -37x2 + 9x4) = 0

Factor a trinomial.
4((1 + -9x2)(4 + -1x2)) = 0

Factor a difference between two squares.
4(((1 + 3x)(1 + -3x))(4 + -1x2)) = 0

Factor a difference between two squares.
4(((2 + x)(2 + -1x))(1 + 3x)(1 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {-0.3333333333, 0.3333333333, -2, 2}

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