2(a+3)+3(a+4)-4(a+5)=5(a+2)

Solution for 2(a+3)+3(a+4)-4(a+5)=5(a+2) equation:

Simplifying
2(a + 3) + 3(a + 4) + -4(a + 5) = 5(a + 2)

Reorder the terms:
2(3 + a) + 3(a + 4) + -4(a + 5) = 5(a + 2)
(3 * 2 + a * 2) + 3(a + 4) + -4(a + 5) = 5(a + 2)
(6 + 2a) + 3(a + 4) + -4(a + 5) = 5(a + 2)

Reorder the terms:
6 + 2a + 3(4 + a) + -4(a + 5) = 5(a + 2)
6 + 2a + (4 * 3 + a * 3) + -4(a + 5) = 5(a + 2)
6 + 2a + (12 + 3a) + -4(a + 5) = 5(a + 2)

Reorder the terms:
6 + 2a + 12 + 3a + -4(5 + a) = 5(a + 2)
6 + 2a + 12 + 3a + (5 * -4 + a * -4) = 5(a + 2)
6 + 2a + 12 + 3a + (-20 + -4a) = 5(a + 2)

Reorder the terms:
6 + 12 + -20 + 2a + 3a + -4a = 5(a + 2)

Combine like terms: 6 + 12 = 18
18 + -20 + 2a + 3a + -4a = 5(a + 2)

Combine like terms: 18 + -20 = -2
-2 + 2a + 3a + -4a = 5(a + 2)

Combine like terms: 2a + 3a = 5a
-2 + 5a + -4a = 5(a + 2)

Combine like terms: 5a + -4a = 1a
-2 + 1a = 5(a + 2)

Reorder the terms:
-2 + 1a = 5(2 + a)
-2 + 1a = (2 * 5 + a * 5)
-2 + 1a = (10 + 5a)

Solving
-2 + 1a = 10 + 5a

Solving for variable 'a'.

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

Add '-5a' to each side of the equation.
-2 + 1a + -5a = 10 + 5a + -5a

Combine like terms: 1a + -5a = -4a
-2 + -4a = 10 + 5a + -5a

Combine like terms: 5a + -5a = 0
-2 + -4a = 10 + 0
-2 + -4a = 10

Add '2' to each side of the equation.
-2 + 2 + -4a = 10 + 2

Combine like terms: -2 + 2 = 0
0 + -4a = 10 + 2
-4a = 10 + 2

Combine like terms: 10 + 2 = 12
-4a = 12

Divide each side by '-4'.
a = -3

Simplifying
a = -3