6x(x+1)=4x

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Solution for 6x(x+1)=4x equation: 


Simplifying
6x(x + 1) = 4x

Reorder the terms:
6x(1 + x) = 4x
(1 * 6x + x * 6x) = 4x
(6x + 6x2) = 4x

Solving
6x + 6x2 = 4x

Solving for variable 'x'.

Reorder the terms:
6x + -4x + 6x2 = 4x + -4x

Combine like terms: 6x + -4x = 2x
2x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + 3x) = 0

Ignore the factor 2.

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 + 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
Solution
x = {0, -0.3333333333}

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