10x(x+1)=x(12x+2)

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Solution for 10x(x+1)=x(12x+2) equation: 


Simplifying
10x(x + 1) = x(12x + 2)

Reorder the terms:
10x(1 + x) = x(12x + 2)
(1 * 10x + x * 10x) = x(12x + 2)
(10x + 10x2) = x(12x + 2)

Reorder the terms:
10x + 10x2 = x(2 + 12x)
10x + 10x2 = (2 * x + 12x * x)
10x + 10x2 = (2x + 12x2)

Solving
10x + 10x2 = 2x + 12x2

Solving for variable 'x'.

Reorder the terms:
10x + -2x + 10x2 + -12x2 = 2x + 12x2 + -2x + -12x2

Combine like terms: 10x + -2x = 8x
8x + 10x2 + -12x2 = 2x + 12x2 + -2x + -12x2

Combine like terms: 10x2 + -12x2 = -2x2
8x + -2x2 = 2x + 12x2 + -2x + -12x2

Reorder the terms:
8x + -2x2 = 2x + -2x + 12x2 + -12x2

Combine like terms: 2x + -2x = 0
8x + -2x2 = 0 + 12x2 + -12x2
8x + -2x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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