4(a-1)+5(a+1)=100

Solution for 4(a-1)+5(a+1)=100 equation:

Simplifying
4(a + -1) + 5(a + 1) = 100

Reorder the terms:
4(-1 + a) + 5(a + 1) = 100
(-1 * 4 + a * 4) + 5(a + 1) = 100
(-4 + 4a) + 5(a + 1) = 100

Reorder the terms:
-4 + 4a + 5(1 + a) = 100
-4 + 4a + (1 * 5 + a * 5) = 100
-4 + 4a + (5 + 5a) = 100

Reorder the terms:
-4 + 5 + 4a + 5a = 100

Combine like terms: -4 + 5 = 1
1 + 4a + 5a = 100

Combine like terms: 4a + 5a = 9a
1 + 9a = 100

Solving
1 + 9a = 100

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + 9a = 100 + -1

Combine like terms: 1 + -1 = 0
0 + 9a = 100 + -1
9a = 100 + -1

Combine like terms: 100 + -1 = 99
9a = 99

Divide each side by '9'.
a = 11

Simplifying
a = 11