2x(2x+1)=6x

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Solution for 2x(2x+1)=6x equation: 


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

Reorder the terms:
2x(1 + 2x) = 6x
(1 * 2x + 2x * 2x) = 6x
(2x + 4x2) = 6x

Solving
2x + 4x2 = 6x

Solving for variable 'x'.

Reorder the terms:
2x + -6x + 4x2 = 6x + -6x

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

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

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

Ignore the factor 4.

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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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