(x-3)(x+5)=(x-1)(x-1)

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Solution for (x-3)(x+5)=(x-1)(x-1) equation: 


Simplifying
(x + -3)(x + 5) = (x + -1)(x + -1)

Reorder the terms:
(-3 + x)(x + 5) = (x + -1)(x + -1)

Reorder the terms:
(-3 + x)(5 + x) = (x + -1)(x + -1)

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) = (x + -1)(x + -1)
((5 * -3 + x * -3) + x(5 + x)) = (x + -1)(x + -1)
((-15 + -3x) + x(5 + x)) = (x + -1)(x + -1)
(-15 + -3x + (5 * x + x * x)) = (x + -1)(x + -1)
(-15 + -3x + (5x + x2)) = (x + -1)(x + -1)

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) = (x + -1)(x + -1)

Reorder the terms:
-15 + 2x + x2 = (-1 + x)(x + -1)

Reorder the terms:
-15 + 2x + x2 = (-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
-15 + 2x + x2 = (-1(-1 + x) + x(-1 + x))
-15 + 2x + x2 = ((-1 * -1 + x * -1) + x(-1 + x))
-15 + 2x + x2 = ((1 + -1x) + x(-1 + x))
-15 + 2x + x2 = (1 + -1x + (-1 * x + x * x))
-15 + 2x + x2 = (1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
-15 + 2x + x2 = (1 + -2x + x2)

Add '-1x2' to each side of the equation.
-15 + 2x + x2 + -1x2 = 1 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 2x + 0 = 1 + -2x + x2 + -1x2
-15 + 2x = 1 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 2x = 1 + -2x + 0
-15 + 2x = 1 + -2x

Solving
-15 + 2x = 1 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
-15 + 2x + 2x = 1 + -2x + 2x

Combine like terms: 2x + 2x = 4x
-15 + 4x = 1 + -2x + 2x

Combine like terms: -2x + 2x = 0
-15 + 4x = 1 + 0
-15 + 4x = 1

Add '15' to each side of the equation.
-15 + 15 + 4x = 1 + 15

Combine like terms: -15 + 15 = 0
0 + 4x = 1 + 15
4x = 1 + 15

Combine like terms: 1 + 15 = 16
4x = 16

Divide each side by '4'.
x = 4

Simplifying
x = 4

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