6x(x-1)=7x(x-1)

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Solution for 6x(x-1)=7x(x-1) equation: 


Simplifying
6x(x + -1) = 7x(x + -1)

Reorder the terms:
6x(-1 + x) = 7x(x + -1)
(-1 * 6x + x * 6x) = 7x(x + -1)
(-6x + 6x2) = 7x(x + -1)

Reorder the terms:
-6x + 6x2 = 7x(-1 + x)
-6x + 6x2 = (-1 * 7x + x * 7x)
-6x + 6x2 = (-7x + 7x2)

Solving
-6x + 6x2 = -7x + 7x2

Solving for variable 'x'.

Reorder the terms:
-6x + 7x + 6x2 + -7x2 = -7x + 7x2 + 7x + -7x2

Combine like terms: -6x + 7x = 1x
1x + 6x2 + -7x2 = -7x + 7x2 + 7x + -7x2

Combine like terms: 6x2 + -7x2 = -1x2
1x + -1x2 = -7x + 7x2 + 7x + -7x2

Reorder the terms:
1x + -1x2 = -7x + 7x + 7x2 + -7x2

Combine like terms: -7x + 7x = 0
1x + -1x2 = 0 + 7x2 + -7x2
1x + -1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

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

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