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

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


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

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

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

Solving
10x + 10x2 = 1x + 12x2

Solving for variable 'x'.

Reorder the terms:
10x + -1x + 10x2 + -12x2 = 1x + 12x2 + -1x + -12x2

Combine like terms: 10x + -1x = 9x
9x + 10x2 + -12x2 = 1x + 12x2 + -1x + -12x2

Combine like terms: 10x2 + -12x2 = -2x2
9x + -2x2 = 1x + 12x2 + -1x + -12x2

Reorder the terms:
9x + -2x2 = 1x + -1x + 12x2 + -12x2

Combine like terms: 1x + -1x = 0
9x + -2x2 = 0 + 12x2 + -12x2
9x + -2x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
9x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -2x) = 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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {0, 4.5}

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