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 = -9
-9 + 4a + -5a = 100

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

Solving
-9 + -1a = 100

Solving for variable 'a'.

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

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

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

Combine like terms: 100 + 9 = 109
-1a = 109

Divide each side by '-1'.
a = -109

Simplifying
a = -109