.9(a+1)=.1(a+9)

Solution for .9(a+1)=.1(a+9) equation:

Simplifying
0.9(a + 1) = 0.1(a + 9)

Reorder the terms:
0.9(1 + a) = 0.1(a + 9)
(1 * 0.9 + a * 0.9) = 0.1(a + 9)
(0.9 + 0.9a) = 0.1(a + 9)

Reorder the terms:
0.9 + 0.9a = 0.1(9 + a)
0.9 + 0.9a = (9 * 0.1 + a * 0.1)
0.9 + 0.9a = (0.9 + 0.1a)

Add '-0.9' to each side of the equation.
0.9 + -0.9 + 0.9a = 0.9 + -0.9 + 0.1a

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + 0.9a = 0.9 + -0.9 + 0.1a
0.9a = 0.9 + -0.9 + 0.1a

Combine like terms: 0.9 + -0.9 = 0.0
0.9a = 0.0 + 0.1a
0.9a = 0.1a

Solving
0.9a = 0.1a

Solving for variable 'a'.

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

Add '-0.1a' to each side of the equation.
0.9a + -0.1a = 0.1a + -0.1a

Combine like terms: 0.9a + -0.1a = 0.8a
0.8a = 0.1a + -0.1a

Combine like terms: 0.1a + -0.1a = 0.0
0.8a = 0.0

Divide each side by '0.8'.
a = 0

Simplifying
a = 0