(x+b)(x-b)=x(x-b)

Solution for (x+b)(x-b)=x(x-b) equation:

Simplifying
(x + b)(x + -1b) = x(x + -1b)

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

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

Multiply (b + x) * (-1b + x)
(b(-1b + x) + x(-1b + x)) = x(x + -1b)
((-1b * b + x * b) + x(-1b + x)) = x(x + -1b)

Reorder the terms:
((bx + -1b2) + x(-1b + x)) = x(x + -1b)
((bx + -1b2) + x(-1b + x)) = x(x + -1b)
(bx + -1b2 + (-1b * x + x * x)) = x(x + -1b)
(bx + -1b2 + (-1bx + x2)) = x(x + -1b)

Reorder the terms:
(bx + -1bx + -1b2 + x2) = x(x + -1b)

Combine like terms: bx + -1bx = 0
(0 + -1b2 + x2) = x(x + -1b)
(-1b2 + x2) = x(x + -1b)

Reorder the terms:
-1b2 + x2 = x(-1b + x)
-1b2 + x2 = (-1b * x + x * x)
-1b2 + x2 = (-1bx + x2)

Add '-1x2' to each side of the equation.
-1b2 + x2 + -1x2 = -1bx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1b2 + 0 = -1bx + x2 + -1x2
-1b2 = -1bx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1b2 = -1bx + 0
-1b2 = -1bx

Solving
-1b2 = -1bx

Solving for variable 'b'.

Reorder the terms:
bx + -1b2 = -1bx + bx

Combine like terms: -1bx + bx = 0
bx + -1b2 = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(x + -1b) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(x + -1b)' equal to zero and attempt to solve:

Simplifying
x + -1b = 0

Reorder the terms:
-1b + x = 0

Solving
-1b + x = 0

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

Add '-1x' to each side of the equation.
-1b + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-1b + 0 = 0 + -1x
-1b = 0 + -1x
Remove the zero:
-1b = -1x

Divide each side by '-1'.
b = x

Simplifying
b = x
Solution
b = {0, x}