v^2+12v+20=(v+10)(v+20)

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Solution for v^2+12v+20=(v+10)(v+20) equation: 


Simplifying
v2 + 12v + 20 = (v + 10)(v + 20)

Reorder the terms:
20 + 12v + v2 = (v + 10)(v + 20)

Reorder the terms:
20 + 12v + v2 = (10 + v)(v + 20)

Reorder the terms:
20 + 12v + v2 = (10 + v)(20 + v)

Multiply (10 + v) * (20 + v)
20 + 12v + v2 = (10(20 + v) + v(20 + v))
20 + 12v + v2 = ((20 * 10 + v * 10) + v(20 + v))
20 + 12v + v2 = ((200 + 10v) + v(20 + v))
20 + 12v + v2 = (200 + 10v + (20 * v + v * v))
20 + 12v + v2 = (200 + 10v + (20v + v2))

Combine like terms: 10v + 20v = 30v
20 + 12v + v2 = (200 + 30v + v2)

Add '-1v2' to each side of the equation.
20 + 12v + v2 + -1v2 = 200 + 30v + v2 + -1v2

Combine like terms: v2 + -1v2 = 0
20 + 12v + 0 = 200 + 30v + v2 + -1v2
20 + 12v = 200 + 30v + v2 + -1v2

Combine like terms: v2 + -1v2 = 0
20 + 12v = 200 + 30v + 0
20 + 12v = 200 + 30v

Solving
20 + 12v = 200 + 30v

Solving for variable 'v'.

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

Add '-30v' to each side of the equation.
20 + 12v + -30v = 200 + 30v + -30v

Combine like terms: 12v + -30v = -18v
20 + -18v = 200 + 30v + -30v

Combine like terms: 30v + -30v = 0
20 + -18v = 200 + 0
20 + -18v = 200

Add '-20' to each side of the equation.
20 + -20 + -18v = 200 + -20

Combine like terms: 20 + -20 = 0
0 + -18v = 200 + -20
-18v = 200 + -20

Combine like terms: 200 + -20 = 180
-18v = 180

Divide each side by '-18'.
v = -10

Simplifying
v = -10

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