(a+10)*(b-10)=a*b-20

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Solution for (a+10)*(b-10)=a*b-20 equation:


Simplifying
(a + 10)(b + -10) = a * b + -20

Reorder the terms:
(10 + a)(b + -10) = a * b + -20

Reorder the terms:
(10 + a)(-10 + b) = a * b + -20

Multiply (10 + a) * (-10 + b)
(10(-10 + b) + a(-10 + b)) = a * b + -20
((-10 * 10 + b * 10) + a(-10 + b)) = a * b + -20
((-100 + 10b) + a(-10 + b)) = a * b + -20
(-100 + 10b + (-10 * a + b * a)) = a * b + -20
(-100 + 10b + (-10a + ab)) = a * b + -20

Reorder the terms:
(-100 + -10a + ab + 10b) = a * b + -20
(-100 + -10a + ab + 10b) = a * b + -20

Multiply a * b
-100 + -10a + ab + 10b = ab + -20

Reorder the terms:
-100 + -10a + ab + 10b = -20 + ab

Add '-1ab' to each side of the equation.
-100 + -10a + ab + -1ab + 10b = -20 + ab + -1ab

Combine like terms: ab + -1ab = 0
-100 + -10a + 0 + 10b = -20 + ab + -1ab
-100 + -10a + 10b = -20 + ab + -1ab

Combine like terms: ab + -1ab = 0
-100 + -10a + 10b = -20 + 0
-100 + -10a + 10b = -20

Solving
-100 + -10a + 10b = -20

Solving for variable 'a'.

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

Add '100' to each side of the equation.
-100 + -10a + 100 + 10b = -20 + 100

Reorder the terms:
-100 + 100 + -10a + 10b = -20 + 100

Combine like terms: -100 + 100 = 0
0 + -10a + 10b = -20 + 100
-10a + 10b = -20 + 100

Combine like terms: -20 + 100 = 80
-10a + 10b = 80

Add '-10b' to each side of the equation.
-10a + 10b + -10b = 80 + -10b

Combine like terms: 10b + -10b = 0
-10a + 0 = 80 + -10b
-10a = 80 + -10b

Divide each side by '-10'.
a = -8 + b

Simplifying
a = -8 + b

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