(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 = 10X
(21 + 10X + X2) = (X + 1)(X + 1)

Reorder the terms:
21 + 10X + X2 = (1 + X)(X + 1)

Reorder the terms:
21 + 10X + X2 = (1 + X)(1 + X)

Multiply (1 + X) * (1 + X)
21 + 10X + X2 = (1(1 + X) + X(1 + X))
21 + 10X + X2 = ((1 * 1 + X * 1) + X(1 + X))
21 + 10X + X2 = ((1 + 1X) + X(1 + X))
21 + 10X + X2 = (1 + 1X + (1 * X + X * X))
21 + 10X + X2 = (1 + 1X + (1X + X2))

Combine like terms: 1X + 1X = 2X
21 + 10X + X2 = (1 + 2X + X2)

Add '-1X2' to each side of the equation.
21 + 10X + X2 + -1X2 = 1 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
21 + 10X + 0 = 1 + 2X + X2 + -1X2
21 + 10X = 1 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
21 + 10X = 1 + 2X + 0
21 + 10X = 1 + 2X

Solving
21 + 10X = 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 + 10X + -2X = 1 + 2X + -2X

Combine like terms: 10X + -2X = 8X
21 + 8X = 1 + 2X + -2X

Combine like terms: 2X + -2X = 0
21 + 8X = 1 + 0
21 + 8X = 1

Add '-21' to each side of the equation.
21 + -21 + 8X = 1 + -21

Combine like terms: 21 + -21 = 0
0 + 8X = 1 + -21
8X = 1 + -21

Combine like terms: 1 + -21 = -20
8X = -20

Divide each side by '8'.
X = -2.5

Simplifying
X = -2.5

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