x^2+4x+a=(x-1)(x+b)

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Solution for x^2+4x+a=(x-1)(x+b) equation:


Simplifying
x2 + 4x + a = (x + -1)(x + b)

Reorder the terms:
a + 4x + x2 = (x + -1)(x + b)

Reorder the terms:
a + 4x + x2 = (-1 + x)(x + b)

Reorder the terms:
a + 4x + x2 = (-1 + x)(b + x)

Multiply (-1 + x) * (b + x)
a + 4x + x2 = (-1(b + x) + x(b + x))
a + 4x + x2 = ((b * -1 + x * -1) + x(b + x))
a + 4x + x2 = ((-1b + -1x) + x(b + x))
a + 4x + x2 = (-1b + -1x + (b * x + x * x))
a + 4x + x2 = (-1b + -1x + (bx + x2))

Reorder the terms:
a + 4x + x2 = (-1b + bx + -1x + x2)
a + 4x + x2 = (-1b + bx + -1x + x2)

Add '-1x2' to each side of the equation.
a + 4x + x2 + -1x2 = -1b + bx + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
a + 4x + 0 = -1b + bx + -1x + x2 + -1x2
a + 4x = -1b + bx + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
a + 4x = -1b + bx + -1x + 0
a + 4x = -1b + bx + -1x

Solving
a + 4x = -1b + bx + -1x

Solving for variable 'a'.

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

Add '-4x' to each side of the equation.
a + 4x + -4x = -1b + bx + -1x + -4x

Combine like terms: 4x + -4x = 0
a + 0 = -1b + bx + -1x + -4x
a = -1b + bx + -1x + -4x

Combine like terms: -1x + -4x = -5x
a = -1b + bx + -5x

Simplifying
a = -1b + bx + -5x

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