(x+6)(x+7)=(11+x)(4+x)

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Solution for (x+6)(x+7)=(11+x)(4+x) equation: 


Simplifying
(x + 6)(x + 7) = (11 + x)(4 + x)

Reorder the terms:
(6 + x)(x + 7) = (11 + x)(4 + x)

Reorder the terms:
(6 + x)(7 + x) = (11 + x)(4 + x)

Multiply (6 + x) * (7 + x)
(6(7 + x) + x(7 + x)) = (11 + x)(4 + x)
((7 * 6 + x * 6) + x(7 + x)) = (11 + x)(4 + x)
((42 + 6x) + x(7 + x)) = (11 + x)(4 + x)
(42 + 6x + (7 * x + x * x)) = (11 + x)(4 + x)
(42 + 6x + (7x + x2)) = (11 + x)(4 + x)

Combine like terms: 6x + 7x = 13x
(42 + 13x + x2) = (11 + x)(4 + x)

Multiply (11 + x) * (4 + x)
42 + 13x + x2 = (11(4 + x) + x(4 + x))
42 + 13x + x2 = ((4 * 11 + x * 11) + x(4 + x))
42 + 13x + x2 = ((44 + 11x) + x(4 + x))
42 + 13x + x2 = (44 + 11x + (4 * x + x * x))
42 + 13x + x2 = (44 + 11x + (4x + x2))

Combine like terms: 11x + 4x = 15x
42 + 13x + x2 = (44 + 15x + x2)

Add '-1x2' to each side of the equation.
42 + 13x + x2 + -1x2 = 44 + 15x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 13x + 0 = 44 + 15x + x2 + -1x2
42 + 13x = 44 + 15x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 13x = 44 + 15x + 0
42 + 13x = 44 + 15x

Solving
42 + 13x = 44 + 15x

Solving for variable 'x'.

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

Add '-15x' to each side of the equation.
42 + 13x + -15x = 44 + 15x + -15x

Combine like terms: 13x + -15x = -2x
42 + -2x = 44 + 15x + -15x

Combine like terms: 15x + -15x = 0
42 + -2x = 44 + 0
42 + -2x = 44

Add '-42' to each side of the equation.
42 + -42 + -2x = 44 + -42

Combine like terms: 42 + -42 = 0
0 + -2x = 44 + -42
-2x = 44 + -42

Combine like terms: 44 + -42 = 2
-2x = 2

Divide each side by '-2'.
x = -1

Simplifying
x = -1

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