y+1.5y-.2=4.2(y-4.5)

Solution for y+1.5y-.2=4.2(y-4.5) equation:

Simplifying
y + 1.5y + -0.2 = 4.2(y + -4.5)

Reorder the terms:
-0.2 + y + 1.5y = 4.2(y + -4.5)

Combine like terms: y + 1.5y = 2.5y
-0.2 + 2.5y = 4.2(y + -4.5)

Reorder the terms:
-0.2 + 2.5y = 4.2(-4.5 + y)
-0.2 + 2.5y = (-4.5 * 4.2 + y * 4.2)
-0.2 + 2.5y = (-18.9 + 4.2y)

Solving
-0.2 + 2.5y = -18.9 + 4.2y

Solving for variable 'y'.

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

Add '-4.2y' to each side of the equation.
-0.2 + 2.5y + -4.2y = -18.9 + 4.2y + -4.2y

Combine like terms: 2.5y + -4.2y = -1.7y
-0.2 + -1.7y = -18.9 + 4.2y + -4.2y

Combine like terms: 4.2y + -4.2y = 0.0
-0.2 + -1.7y = -18.9 + 0.0
-0.2 + -1.7y = -18.9

Add '0.2' to each side of the equation.
-0.2 + 0.2 + -1.7y = -18.9 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.7y = -18.9 + 0.2
-1.7y = -18.9 + 0.2

Combine like terms: -18.9 + 0.2 = -18.7
-1.7y = -18.7

Divide each side by '-1.7'.
y = 11

Simplifying
y = 11