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

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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 = 2x
-21 + 4x + x2 = (1 + 2x + x2)

Add '-1x2' to each side of the equation.
-21 + 4x + x2 + -1x2 = 1 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x + 0 = 1 + 2x + x2 + -1x2
-21 + 4x = 1 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x = 1 + 2x + 0
-21 + 4x = 1 + 2x

Solving
-21 + 4x = 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.
-21 + 4x + -2x = 1 + 2x + -2x

Combine like terms: 4x + -2x = 2x
-21 + 2x = 1 + 2x + -2x

Combine like terms: 2x + -2x = 0
-21 + 2x = 1 + 0
-21 + 2x = 1

Add '21' to each side of the equation.
-21 + 21 + 2x = 1 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 1 + 21
2x = 1 + 21

Combine like terms: 1 + 21 = 22
2x = 22

Divide each side by '2'.
x = 11

Simplifying
x = 11

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