ab+10+5b+2a=(a+5)(b+2)

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Solution for ab+10+5b+2a=(a+5)(b+2) equation: 


Simplifying
ab + 10 + 5b + 2a = (a + 5)(b + 2)

Reorder the terms:
10 + 2a + ab + 5b = (a + 5)(b + 2)

Reorder the terms:
10 + 2a + ab + 5b = (5 + a)(b + 2)

Reorder the terms:
10 + 2a + ab + 5b = (5 + a)(2 + b)

Multiply (5 + a) * (2 + b)
10 + 2a + ab + 5b = (5(2 + b) + a(2 + b))
10 + 2a + ab + 5b = ((2 * 5 + b * 5) + a(2 + b))
10 + 2a + ab + 5b = ((10 + 5b) + a(2 + b))
10 + 2a + ab + 5b = (10 + 5b + (2 * a + b * a))
10 + 2a + ab + 5b = (10 + 5b + (2a + ab))

Reorder the terms:
10 + 2a + ab + 5b = (10 + 2a + ab + 5b)
10 + 2a + ab + 5b = (10 + 2a + ab + 5b)

Add '-10' to each side of the equation.
10 + 2a + ab + -10 + 5b = 10 + 2a + ab + -10 + 5b

Reorder the terms:
10 + -10 + 2a + ab + 5b = 10 + 2a + ab + -10 + 5b

Combine like terms: 10 + -10 = 0
0 + 2a + ab + 5b = 10 + 2a + ab + -10 + 5b
2a + ab + 5b = 10 + 2a + ab + -10 + 5b

Reorder the terms:
2a + ab + 5b = 10 + -10 + 2a + ab + 5b

Combine like terms: 10 + -10 = 0
2a + ab + 5b = 0 + 2a + ab + 5b
2a + ab + 5b = 2a + ab + 5b

Add '-2a' to each side of the equation.
2a + ab + -2a + 5b = 2a + ab + -2a + 5b

Reorder the terms:
2a + -2a + ab + 5b = 2a + ab + -2a + 5b

Combine like terms: 2a + -2a = 0
0 + ab + 5b = 2a + ab + -2a + 5b
ab + 5b = 2a + ab + -2a + 5b

Reorder the terms:
ab + 5b = 2a + -2a + ab + 5b

Combine like terms: 2a + -2a = 0
ab + 5b = 0 + ab + 5b
ab + 5b = ab + 5b

Add '-1ab' to each side of the equation.
ab + -1ab + 5b = ab + -1ab + 5b

Combine like terms: ab + -1ab = 0
0 + 5b = ab + -1ab + 5b
5b = ab + -1ab + 5b

Combine like terms: ab + -1ab = 0
5b = 0 + 5b
5b = 5b

Add '-5b' to each side of the equation.
5b + -5b = 5b + -5b

Combine like terms: 5b + -5b = 0
0 = 5b + -5b

Combine like terms: 5b + -5b = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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