x(x+6)+48=(x+1)(x+7)

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Solution for x(x+6)+48=(x+1)(x+7) equation: 


Simplifying
x(x + 6) + 48 = (x + 1)(x + 7)

Reorder the terms:
x(6 + x) + 48 = (x + 1)(x + 7)
(6 * x + x * x) + 48 = (x + 1)(x + 7)
(6x + x2) + 48 = (x + 1)(x + 7)

Reorder the terms:
48 + 6x + x2 = (x + 1)(x + 7)

Reorder the terms:
48 + 6x + x2 = (1 + x)(x + 7)

Reorder the terms:
48 + 6x + x2 = (1 + x)(7 + x)

Multiply (1 + x) * (7 + x)
48 + 6x + x2 = (1(7 + x) + x(7 + x))
48 + 6x + x2 = ((7 * 1 + x * 1) + x(7 + x))
48 + 6x + x2 = ((7 + 1x) + x(7 + x))
48 + 6x + x2 = (7 + 1x + (7 * x + x * x))
48 + 6x + x2 = (7 + 1x + (7x + x2))

Combine like terms: 1x + 7x = 8x
48 + 6x + x2 = (7 + 8x + x2)

Add '-1x2' to each side of the equation.
48 + 6x + x2 + -1x2 = 7 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + 6x + 0 = 7 + 8x + x2 + -1x2
48 + 6x = 7 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + 6x = 7 + 8x + 0
48 + 6x = 7 + 8x

Solving
48 + 6x = 7 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
48 + 6x + -8x = 7 + 8x + -8x

Combine like terms: 6x + -8x = -2x
48 + -2x = 7 + 8x + -8x

Combine like terms: 8x + -8x = 0
48 + -2x = 7 + 0
48 + -2x = 7

Add '-48' to each side of the equation.
48 + -48 + -2x = 7 + -48

Combine like terms: 48 + -48 = 0
0 + -2x = 7 + -48
-2x = 7 + -48

Combine like terms: 7 + -48 = -41
-2x = -41

Divide each side by '-2'.
x = 20.5

Simplifying
x = 20.5

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