14x(x+12)=22x(x+10)

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Solution for 14x(x+12)=22x(x+10) equation: 


Simplifying
14x(x + 12) = 22x(x + 10)

Reorder the terms:
14x(12 + x) = 22x(x + 10)
(12 * 14x + x * 14x) = 22x(x + 10)
(168x + 14x2) = 22x(x + 10)

Reorder the terms:
168x + 14x2 = 22x(10 + x)
168x + 14x2 = (10 * 22x + x * 22x)
168x + 14x2 = (220x + 22x2)

Solving
168x + 14x2 = 220x + 22x2

Solving for variable 'x'.

Reorder the terms:
168x + -220x + 14x2 + -22x2 = 220x + 22x2 + -220x + -22x2

Combine like terms: 168x + -220x = -52x
-52x + 14x2 + -22x2 = 220x + 22x2 + -220x + -22x2

Combine like terms: 14x2 + -22x2 = -8x2
-52x + -8x2 = 220x + 22x2 + -220x + -22x2

Reorder the terms:
-52x + -8x2 = 220x + -220x + 22x2 + -22x2

Combine like terms: 220x + -220x = 0
-52x + -8x2 = 0 + 22x2 + -22x2
-52x + -8x2 = 22x2 + -22x2

Combine like terms: 22x2 + -22x2 = 0
-52x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(13 + 2x) = 0

Ignore the factor -4.

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 '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {0, -6.5}

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