(3*0.5+1)(0.5+a)-3(0.5-1)(0.5-a)=4

Solution for (3*0.5+1)(0.5+a)-3(0.5-1)(0.5-a)=4 equation:

Simplifying
(3 * 0.5 + 1)(0.5 + a) + -3(0.5 + -1)(0.5 + -1a) = 4

Multiply 3 * 0.5
(1.5 + 1)(0.5 + a) + -3(0.5 + -1)(0.5 + -1a) = 4

Combine like terms: 1.5 + 1 = 2.5
(2.5)(0.5 + a) + -3(0.5 + -1)(0.5 + -1a) = 4
(0.5 * 2.5 + a * 2.5) + -3(0.5 + -1)(0.5 + -1a) = 4
(1.25 + 2.5a) + -3(0.5 + -1)(0.5 + -1a) = 4

Combine like terms: 0.5 + -1 = -0.5
1.25 + 2.5a + -3(-0.5)(0.5 + -1a) = 4

Multiply -3 * -0.5
1.25 + 2.5a + 1.5(0.5 + -1a) = 4
1.25 + 2.5a + (0.5 * 1.5 + -1a * 1.5) = 4
1.25 + 2.5a + (0.75 + -1.5a) = 4

Reorder the terms:
1.25 + 0.75 + 2.5a + -1.5a = 4

Combine like terms: 1.25 + 0.75 = 2
2 + 2.5a + -1.5a = 4

Combine like terms: 2.5a + -1.5a = 1a
2 + 1a = 4

Solving
2 + 1a = 4

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + 1a = 4 + -2

Combine like terms: 2 + -2 = 0
0 + 1a = 4 + -2
1a = 4 + -2

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

Divide each side by '1'.
a = 2

Simplifying
a = 2