(x+7)(x-3)=(x+1)(x-1)

Solution for (x+7)(x-3)=(x+1)(x-1) equation:

Simplifying
(x + 7)(x + -3) = (x + 1)(x + -1)

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

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

Multiply (7 + x) * (-3 + x)
(7(-3 + x) + x(-3 + x)) = (x + 1)(x + -1)
((-3 * 7 + x * 7) + x(-3 + x)) = (x + 1)(x + -1)
((-21 + 7x) + x(-3 + x)) = (x + 1)(x + -1)
(-21 + 7x + (-3 * x + x * x)) = (x + 1)(x + -1)
(-21 + 7x + (-3x + x2)) = (x + 1)(x + -1)

Combine like terms: 7x + -3x = 4x
(-21 + 4x + x2) = (x + 1)(x + -1)

Reorder the terms:
-21 + 4x + x2 = (1 + x)(x + -1)

Reorder the terms:
-21 + 4x + x2 = (1 + x)(-1 + x)

Multiply (1 + x) * (-1 + x)
-21 + 4x + x2 = (1(-1 + x) + x(-1 + x))
-21 + 4x + x2 = ((-1 * 1 + x * 1) + x(-1 + x))
-21 + 4x + x2 = ((-1 + 1x) + x(-1 + x))
-21 + 4x + x2 = (-1 + 1x + (-1 * x + x * x))
-21 + 4x + x2 = (-1 + 1x + (-1x + x2))

Combine like terms: 1x + -1x = 0
-21 + 4x + x2 = (-1 + 0 + x2)
-21 + 4x + x2 = (-1 + x2)

Add '-1x2' to each side of the equation.
-21 + 4x + x2 + -1x2 = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x + 0 = -1 + x2 + -1x2
-21 + 4x = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x = -1 + 0
-21 + 4x = -1

Solving
-21 + 4x = -1

Solving for variable 'x'.

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

Add '21' to each side of the equation.
-21 + 21 + 4x = -1 + 21

Combine like terms: -21 + 21 = 0
0 + 4x = -1 + 21
4x = -1 + 21

Combine like terms: -1 + 21 = 20
4x = 20

Divide each side by '4'.
x = 5

Simplifying
x = 5