2[3+(b+3)x]+2bx=3-3(2x-1)

Solution for 2[3+(b+3)x]+2bx=3-3(2x-1) equation:

Simplifying
2[3 + (b + 3) * x] + 2bx = 3 + -3(2x + -1)

Reorder the terms:
2[3 + (3 + b) * x] + 2bx = 3 + -3(2x + -1)

Reorder the terms for easier multiplication:
2[3 + x(3 + b)] + 2bx = 3 + -3(2x + -1)
2[3 + (3 * x + b * x)] + 2bx = 3 + -3(2x + -1)

Reorder the terms:
2[3 + (bx + 3x)] + 2bx = 3 + -3(2x + -1)
2[3 + (bx + 3x)] + 2bx = 3 + -3(2x + -1)
[3 * 2 + bx * 2 + 3x * 2] + 2bx = 3 + -3(2x + -1)
[6 + 2bx + 6x] + 2bx = 3 + -3(2x + -1)

Reorder the terms:
6 + 2bx + 2bx + 6x = 3 + -3(2x + -1)

Combine like terms: 2bx + 2bx = 4bx
6 + 4bx + 6x = 3 + -3(2x + -1)

Reorder the terms:
6 + 4bx + 6x = 3 + -3(-1 + 2x)
6 + 4bx + 6x = 3 + (-1 * -3 + 2x * -3)
6 + 4bx + 6x = 3 + (3 + -6x)

Combine like terms: 3 + 3 = 6
6 + 4bx + 6x = 6 + -6x

Add '-6' to each side of the equation.
6 + 4bx + -6 + 6x = 6 + -6 + -6x

Reorder the terms:
6 + -6 + 4bx + 6x = 6 + -6 + -6x

Combine like terms: 6 + -6 = 0
0 + 4bx + 6x = 6 + -6 + -6x
4bx + 6x = 6 + -6 + -6x

Combine like terms: 6 + -6 = 0
4bx + 6x = 0 + -6x
4bx + 6x = -6x

Solving
4bx + 6x = -6x

Solving for variable 'b'.

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

Add '-6x' to each side of the equation.
4bx + 6x + -6x = -6x + -6x

Combine like terms: 6x + -6x = 0
4bx + 0 = -6x + -6x
4bx = -6x + -6x

Combine like terms: -6x + -6x = -12x
4bx = -12x

Divide each side by '4x'.
b = -3

Simplifying
b = -3