.45(5a-8)-13=15+(-3)(1.6a+5)

Solution for .45(5a-8)-13=15+(-3)(1.6a+5) equation:

Simplifying
0.45(5a + -8) + -13 = 15 + (-3)(1.6a + 5)

Reorder the terms:
0.45(-8 + 5a) + -13 = 15 + (-3)(1.6a + 5)
(-8 * 0.45 + 5a * 0.45) + -13 = 15 + (-3)(1.6a + 5)
(-3.6 + 2.25a) + -13 = 15 + (-3)(1.6a + 5)

Reorder the terms:
-3.6 + -13 + 2.25a = 15 + (-3)(1.6a + 5)

Combine like terms: -3.6 + -13 = -16.6
-16.6 + 2.25a = 15 + (-3)(1.6a + 5)

Reorder the terms:
-16.6 + 2.25a = 15 + -3(5 + 1.6a)
-16.6 + 2.25a = 15 + (5 * -3 + 1.6a * -3)
-16.6 + 2.25a = 15 + (-15 + -4.8a)

Combine like terms: 15 + -15 = 0
-16.6 + 2.25a = 0 + -4.8a
-16.6 + 2.25a = -4.8a

Solving
-16.6 + 2.25a = -4.8a

Solving for variable 'a'.

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

Add '4.8a' to each side of the equation.
-16.6 + 2.25a + 4.8a = -4.8a + 4.8a

Combine like terms: 2.25a + 4.8a = 7.05a
-16.6 + 7.05a = -4.8a + 4.8a

Combine like terms: -4.8a + 4.8a = 0.0
-16.6 + 7.05a = 0.0

Add '16.6' to each side of the equation.
-16.6 + 16.6 + 7.05a = 0.0 + 16.6

Combine like terms: -16.6 + 16.6 = 0.0
0.0 + 7.05a = 0.0 + 16.6
7.05a = 0.0 + 16.6

Combine like terms: 0.0 + 16.6 = 16.6
7.05a = 16.6

Divide each side by '7.05'.
a = 2.354609929

Simplifying
a = 2.354609929