(x-5)(xb+2x+1)=x(x+1)(x-4)

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Solution for (x-5)(xb+2x+1)=x(x+1)(x-4) equation:


Simplifying
(x + -5)(xb + 2x + 1) = x(x + 1)(x + -4)

Reorder the terms:
(-5 + x)(xb + 2x + 1) = x(x + 1)(x + -4)

Reorder the terms:
(-5 + x)(1 + bx + 2x) = x(x + 1)(x + -4)

Multiply (-5 + x) * (1 + bx + 2x)
(-5(1 + bx + 2x) + x(1 + bx + 2x)) = x(x + 1)(x + -4)
((1 * -5 + bx * -5 + 2x * -5) + x(1 + bx + 2x)) = x(x + 1)(x + -4)
((-5 + -5bx + -10x) + x(1 + bx + 2x)) = x(x + 1)(x + -4)
(-5 + -5bx + -10x + (1 * x + bx * x + 2x * x)) = x(x + 1)(x + -4)

Reorder the terms:
(-5 + -5bx + -10x + (bx2 + 1x + 2x2)) = x(x + 1)(x + -4)
(-5 + -5bx + -10x + (bx2 + 1x + 2x2)) = x(x + 1)(x + -4)

Reorder the terms:
(-5 + -5bx + bx2 + -10x + 1x + 2x2) = x(x + 1)(x + -4)

Combine like terms: -10x + 1x = -9x
(-5 + -5bx + bx2 + -9x + 2x2) = x(x + 1)(x + -4)

Reorder the terms:
-5 + -5bx + bx2 + -9x + 2x2 = x(1 + x)(x + -4)

Reorder the terms:
-5 + -5bx + bx2 + -9x + 2x2 = x(1 + x)(-4 + x)

Multiply (1 + x) * (-4 + x)
-5 + -5bx + bx2 + -9x + 2x2 = x(1(-4 + x) + x(-4 + x))
-5 + -5bx + bx2 + -9x + 2x2 = x((-4 * 1 + x * 1) + x(-4 + x))
-5 + -5bx + bx2 + -9x + 2x2 = x((-4 + 1x) + x(-4 + x))
-5 + -5bx + bx2 + -9x + 2x2 = x(-4 + 1x + (-4 * x + x * x))
-5 + -5bx + bx2 + -9x + 2x2 = x(-4 + 1x + (-4x + x2))

Combine like terms: 1x + -4x = -3x
-5 + -5bx + bx2 + -9x + 2x2 = x(-4 + -3x + x2)
-5 + -5bx + bx2 + -9x + 2x2 = (-4 * x + -3x * x + x2 * x)
-5 + -5bx + bx2 + -9x + 2x2 = (-4x + -3x2 + x3)

Solving
-5 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + x3

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + -5bx + bx2 + -9x + 5 + 2x2 = -4x + -3x2 + 5 + x3

Reorder the terms:
-5 + 5 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3

Combine like terms: -5 + 5 = 0
0 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3
-5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3

Reorder the terms:
-5bx + bx2 + -9x + 2x2 = 5 + -4x + -3x2 + x3

Add '9x' to each side of the equation.
-5bx + bx2 + -9x + 9x + 2x2 = 5 + -4x + -3x2 + 9x + x3

Combine like terms: -9x + 9x = 0
-5bx + bx2 + 0 + 2x2 = 5 + -4x + -3x2 + 9x + x3
-5bx + bx2 + 2x2 = 5 + -4x + -3x2 + 9x + x3

Reorder the terms:
-5bx + bx2 + 2x2 = 5 + -4x + 9x + -3x2 + x3

Combine like terms: -4x + 9x = 5x
-5bx + bx2 + 2x2 = 5 + 5x + -3x2 + x3

Add '-2x2' to each side of the equation.
-5bx + bx2 + 2x2 + -2x2 = 5 + 5x + -3x2 + -2x2 + x3

Combine like terms: 2x2 + -2x2 = 0
-5bx + bx2 + 0 = 5 + 5x + -3x2 + -2x2 + x3
-5bx + bx2 = 5 + 5x + -3x2 + -2x2 + x3

Combine like terms: -3x2 + -2x2 = -5x2
-5bx + bx2 = 5 + 5x + -5x2 + x3

Reorder the terms:
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5 + 5x + -5x2 + x3 + -5 + -5x + 5x2 + -1x3

Reorder the terms:
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5 + -5 + 5x + -5x + -5x2 + 5x2 + x3 + -1x3

Combine like terms: 5 + -5 = 0
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + 5x + -5x + -5x2 + 5x2 + x3 + -1x3
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5x + -5x + -5x2 + 5x2 + x3 + -1x3

Combine like terms: 5x + -5x = 0
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + -5x2 + 5x2 + x3 + -1x3
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = -5x2 + 5x2 + x3 + -1x3

Combine like terms: -5x2 + 5x2 = 0
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + x3 + -1x3
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0

The solution to this equation could not be determined.

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