6x=x(2x+2)

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


Simplifying
6x = x(2x + 2)

Reorder the terms:
6x = x(2 + 2x)
6x = (2 * x + 2x * x)
6x = (2x + 2x2)

Solving
6x = 2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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