6x(x+2)=5x-x

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Solution for 6x(x+2)=5x-x equation: 


Simplifying
6x(x + 2) = 5x + -1x

Reorder the terms:
6x(2 + x) = 5x + -1x
(2 * 6x + x * 6x) = 5x + -1x
(12x + 6x2) = 5x + -1x

Combine like terms: 5x + -1x = 4x
12x + 6x2 = 4x

Solving
12x + 6x2 = 4x

Solving for variable 'x'.

Reorder the terms:
12x + -4x + 6x2 = 4x + -4x

Combine like terms: 12x + -4x = 8x
8x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + 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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {0, -1.333333333}

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