3x=x(2-4x)

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Solution for 3x=x(2-4x) equation: 


Simplifying
3x = x(2 + -4x)
3x = (2 * x + -4x * x)
3x = (2x + -4x2)

Solving
3x = 2x + -4x2

Solving for variable 'x'.

Combine like terms: 3x + -2x = 1x
1x + 4x2 = 2x + -4x2 + -2x + 4x2

Reorder the terms:
1x + 4x2 = 2x + -2x + -4x2 + 4x2

Combine like terms: 2x + -2x = 0
1x + 4x2 = 0 + -4x2 + 4x2
1x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
1x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 4x) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {0, -0.25}

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