5(a-1)+3(2-7a)=a-(a-33)

Solution for 5(a-1)+3(2-7a)=a-(a-33) equation:

Simplifying
5(a + -1) + 3(2 + -7a) = a + -1(a + -33)

Reorder the terms:
5(-1 + a) + 3(2 + -7a) = a + -1(a + -33)
(-1 * 5 + a * 5) + 3(2 + -7a) = a + -1(a + -33)
(-5 + 5a) + 3(2 + -7a) = a + -1(a + -33)
-5 + 5a + (2 * 3 + -7a * 3) = a + -1(a + -33)
-5 + 5a + (6 + -21a) = a + -1(a + -33)

Reorder the terms:
-5 + 6 + 5a + -21a = a + -1(a + -33)

Combine like terms: -5 + 6 = 1
1 + 5a + -21a = a + -1(a + -33)

Combine like terms: 5a + -21a = -16a
1 + -16a = a + -1(a + -33)

Reorder the terms:
1 + -16a = a + -1(-33 + a)
1 + -16a = a + (-33 * -1 + a * -1)
1 + -16a = a + (33 + -1a)

Reorder the terms:
1 + -16a = 33 + a + -1a

Combine like terms: a + -1a = 0
1 + -16a = 33 + 0
1 + -16a = 33

Solving
1 + -16a = 33

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 + -16a = 33 + -1

Combine like terms: 1 + -1 = 0
0 + -16a = 33 + -1
-16a = 33 + -1

Combine like terms: 33 + -1 = 32
-16a = 32

Divide each side by '-16'.
a = -2

Simplifying
a = -2