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

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


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

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

Remove parenthesis around (10x)
2x + 12x2 = 10x(x + 1)

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
-8x + 2x2 = 10x + -10x + 10x2 + -10x2

Combine like terms: 10x + -10x = 0
-8x + 2x2 = 0 + 10x2 + -10x2
-8x + 2x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-8x + 2x2 = 0

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

Simplifying
-4 + x = 0

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

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

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

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

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