f(0)=36x^4-16x^2

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Solution for f(0)=36x^4-16x^2 equation: 


Simplifying
f(0) = 36x4 + -16x2

Reorder the terms for easier multiplication:
0f = 36x4 + -16x2

Anything times zero is zero.
0f = 36x4 + -16x2

Reorder the terms:
0 = -16x2 + 36x4

Solving
0 = -16x2 + 36x4

Solving for variable 'x'.
Remove the zero:
16x2 + -36x4 = -16x2 + 36x4 + 16x2 + -36x4

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

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

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

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

Factor a difference between two squares.
4x2((2 + 3x)(2 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, -0.6666666667, 0.6666666667}

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