(a+b)(x-3)-(a+b)(x+1)=0

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Solution for (a+b)(x-3)-(a+b)(x+1)=0 equation:


Simplifying
(a + b)(x + -3) + -1(a + b)(x + 1) = 0

Reorder the terms:
(a + b)(-3 + x) + -1(a + b)(x + 1) = 0

Multiply (a + b) * (-3 + x)
(a(-3 + x) + b(-3 + x)) + -1(a + b)(x + 1) = 0
((-3 * a + x * a) + b(-3 + x)) + -1(a + b)(x + 1) = 0
((-3a + ax) + b(-3 + x)) + -1(a + b)(x + 1) = 0
(-3a + ax + (-3 * b + x * b)) + -1(a + b)(x + 1) = 0
(-3a + ax + (-3b + bx)) + -1(a + b)(x + 1) = 0
(-3a + ax + -3b + bx) + -1(a + b)(x + 1) = 0

Reorder the terms:
-3a + ax + -3b + bx + -1(a + b)(1 + x) = 0

Multiply (a + b) * (1 + x)
-3a + ax + -3b + bx + -1(a(1 + x) + b(1 + x)) = 0
-3a + ax + -3b + bx + -1((1 * a + x * a) + b(1 + x)) = 0
-3a + ax + -3b + bx + -1((1a + ax) + b(1 + x)) = 0
-3a + ax + -3b + bx + -1(1a + ax + (1 * b + x * b)) = 0
-3a + ax + -3b + bx + -1(1a + ax + (1b + bx)) = 0
-3a + ax + -3b + bx + -1(1a + ax + 1b + bx) = 0
-3a + ax + -3b + bx + (1a * -1 + ax * -1 + 1b * -1 + bx * -1) = 0
-3a + ax + -3b + bx + (-1a + -1ax + -1b + -1bx) = 0

Reorder the terms:
-3a + -1a + ax + -1ax + -3b + -1b + bx + -1bx = 0

Combine like terms: -3a + -1a = -4a
-4a + ax + -1ax + -3b + -1b + bx + -1bx = 0

Combine like terms: ax + -1ax = 0
-4a + 0 + -3b + -1b + bx + -1bx = 0
-4a + -3b + -1b + bx + -1bx = 0

Combine like terms: -3b + -1b = -4b
-4a + -4b + bx + -1bx = 0

Combine like terms: bx + -1bx = 0
-4a + -4b + 0 = 0
-4a + -4b = 0

Solving
-4a + -4b = 0

Solving for variable 'a'.

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

Add '4b' to each side of the equation.
-4a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
-4a + 0 = 0 + 4b
-4a = 0 + 4b
Remove the zero:
-4a = 4b

Divide each side by '-4'.
a = -1b

Simplifying
a = -1b

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