x(x+2)=10x(x+14)

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Solution for x(x+2)=10x(x+14) equation: 


Simplifying
x(x + 2) = 10x(x + 14)

Reorder the terms:
x(2 + x) = 10x(x + 14)
(2 * x + x * x) = 10x(x + 14)
(2x + x2) = 10x(x + 14)

Reorder the terms:
2x + x2 = 10x(14 + x)
2x + x2 = (14 * 10x + x * 10x)
2x + x2 = (140x + 10x2)

Solving
2x + x2 = 140x + 10x2

Solving for variable 'x'.

Reorder the terms:
2x + -140x + x2 + -10x2 = 140x + 10x2 + -140x + -10x2

Combine like terms: 2x + -140x = -138x
-138x + x2 + -10x2 = 140x + 10x2 + -140x + -10x2

Combine like terms: x2 + -10x2 = -9x2
-138x + -9x2 = 140x + 10x2 + -140x + -10x2

Reorder the terms:
-138x + -9x2 = 140x + -140x + 10x2 + -10x2

Combine like terms: 140x + -140x = 0
-138x + -9x2 = 0 + 10x2 + -10x2
-138x + -9x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-138x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-3x'.
-3x(46 + 3x) = 0

Ignore the factor -3.

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 '(46 + 3x)' equal to zero and attempt to solve:

Simplifying
46 + 3x = 0

Solving
46 + 3x = 0

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

Add '-46' to each side of the equation.
46 + -46 + 3x = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 3x = 0 + -46
3x = 0 + -46

Combine like terms: 0 + -46 = -46
3x = -46

Divide each side by '3'.
x = -15.33333333

Simplifying
x = -15.33333333
Solution
x = {0, -15.33333333}

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