(x-3)(x+5)=2(x-3)

Solution for (x-3)(x+5)=2(x-3) equation:

Simplifying
(x + -3)(x + 5) = 2(x + -3)

Reorder the terms:
(-3 + x)(x + 5) = 2(x + -3)

Reorder the terms:
(-3 + x)(5 + x) = 2(x + -3)

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) = 2(x + -3)
((5 * -3 + x * -3) + x(5 + x)) = 2(x + -3)
((-15 + -3x) + x(5 + x)) = 2(x + -3)
(-15 + -3x + (5 * x + x * x)) = 2(x + -3)
(-15 + -3x + (5x + x2)) = 2(x + -3)

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) = 2(x + -3)

Reorder the terms:
-15 + 2x + x2 = 2(-3 + x)
-15 + 2x + x2 = (-3 * 2 + x * 2)
-15 + 2x + x2 = (-6 + 2x)

Add '-2x' to each side of the equation.
-15 + 2x + -2x + x2 = -6 + 2x + -2x

Combine like terms: 2x + -2x = 0
-15 + 0 + x2 = -6 + 2x + -2x
-15 + x2 = -6 + 2x + -2x

Combine like terms: 2x + -2x = 0
-15 + x2 = -6 + 0
-15 + x2 = -6

Solving
-15 + x2 = -6

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x2 = -6 + 15

Combine like terms: -15 + 15 = 0
0 + x2 = -6 + 15
x2 = -6 + 15

Combine like terms: -6 + 15 = 9
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}