(x+13)(x+2)=(x+8)(x+5)

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Solution for (x+13)(x+2)=(x+8)(x+5) equation:


Simplifying
(x + 13)(x + 2) = (x + 8)(x + 5)

Reorder the terms:
(13 + x)(x + 2) = (x + 8)(x + 5)

Reorder the terms:
(13 + x)(2 + x) = (x + 8)(x + 5)

Multiply (13 + x) * (2 + x)
(13(2 + x) + x(2 + x)) = (x + 8)(x + 5)
((2 * 13 + x * 13) + x(2 + x)) = (x + 8)(x + 5)
((26 + 13x) + x(2 + x)) = (x + 8)(x + 5)
(26 + 13x + (2 * x + x * x)) = (x + 8)(x + 5)
(26 + 13x + (2x + x2)) = (x + 8)(x + 5)

Combine like terms: 13x + 2x = 15x
(26 + 15x + x2) = (x + 8)(x + 5)

Reorder the terms:
26 + 15x + x2 = (8 + x)(x + 5)

Reorder the terms:
26 + 15x + x2 = (8 + x)(5 + x)

Multiply (8 + x) * (5 + x)
26 + 15x + x2 = (8(5 + x) + x(5 + x))
26 + 15x + x2 = ((5 * 8 + x * 8) + x(5 + x))
26 + 15x + x2 = ((40 + 8x) + x(5 + x))
26 + 15x + x2 = (40 + 8x + (5 * x + x * x))
26 + 15x + x2 = (40 + 8x + (5x + x2))

Combine like terms: 8x + 5x = 13x
26 + 15x + x2 = (40 + 13x + x2)

Add '-1x2' to each side of the equation.
26 + 15x + x2 + -1x2 = 40 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
26 + 15x + 0 = 40 + 13x + x2 + -1x2
26 + 15x = 40 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
26 + 15x = 40 + 13x + 0
26 + 15x = 40 + 13x

Solving
26 + 15x = 40 + 13x

Solving for variable 'x'.

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

Add '-13x' to each side of the equation.
26 + 15x + -13x = 40 + 13x + -13x

Combine like terms: 15x + -13x = 2x
26 + 2x = 40 + 13x + -13x

Combine like terms: 13x + -13x = 0
26 + 2x = 40 + 0
26 + 2x = 40

Add '-26' to each side of the equation.
26 + -26 + 2x = 40 + -26

Combine like terms: 26 + -26 = 0
0 + 2x = 40 + -26
2x = 40 + -26

Combine like terms: 40 + -26 = 14
2x = 14

Divide each side by '2'.
x = 7

Simplifying
x = 7

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