(x+k)(2x+5)=x^2+13x+20

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Solution for (x+k)(2x+5)=x^2+13x+20 equation: 


Simplifying
(x + k)(2x + 5) = x2 + 13x + 20

Reorder the terms:
(k + x)(2x + 5) = x2 + 13x + 20

Reorder the terms:
(k + x)(5 + 2x) = x2 + 13x + 20

Multiply (k + x) * (5 + 2x)
(k(5 + 2x) + x(5 + 2x)) = x2 + 13x + 20
((5 * k + 2x * k) + x(5 + 2x)) = x2 + 13x + 20
((5k + 2kx) + x(5 + 2x)) = x2 + 13x + 20
(5k + 2kx + (5 * x + 2x * x)) = x2 + 13x + 20
(5k + 2kx + (5x + 2x2)) = x2 + 13x + 20
(5k + 2kx + 5x + 2x2) = x2 + 13x + 20

Reorder the terms:
5k + 2kx + 5x + 2x2 = 20 + 13x + x2

Solving
5k + 2kx + 5x + 2x2 = 20 + 13x + x2

Solving for variable 'k'.

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

Add '-5x' to each side of the equation.
5k + 2kx + 5x + -5x + 2x2 = 20 + 13x + -5x + x2

Combine like terms: 5x + -5x = 0
5k + 2kx + 0 + 2x2 = 20 + 13x + -5x + x2
5k + 2kx + 2x2 = 20 + 13x + -5x + x2

Combine like terms: 13x + -5x = 8x
5k + 2kx + 2x2 = 20 + 8x + x2

Add '-2x2' to each side of the equation.
5k + 2kx + 2x2 + -2x2 = 20 + 8x + x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5k + 2kx + 0 = 20 + 8x + x2 + -2x2
5k + 2kx = 20 + 8x + x2 + -2x2

Combine like terms: x2 + -2x2 = -1x2
5k + 2kx = 20 + 8x + -1x2

Reorder the terms:
-20 + 5k + 2kx + -8x + x2 = 20 + 8x + -1x2 + -20 + -8x + x2

Reorder the terms:
-20 + 5k + 2kx + -8x + x2 = 20 + -20 + 8x + -8x + -1x2 + x2

Combine like terms: 20 + -20 = 0
-20 + 5k + 2kx + -8x + x2 = 0 + 8x + -8x + -1x2 + x2
-20 + 5k + 2kx + -8x + x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
-20 + 5k + 2kx + -8x + x2 = 0 + -1x2 + x2
-20 + 5k + 2kx + -8x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-20 + 5k + 2kx + -8x + x2 = 0

The solution to this equation could not be determined.

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