(x+1)(x+3)=(x-4)(x+5)

Solution for (x+1)(x+3)=(x-4)(x+5) equation:

Simplifying
(x + 1)(x + 3) = (x + -4)(x + 5)

Reorder the terms:
(1 + x)(x + 3) = (x + -4)(x + 5)

Reorder the terms:
(1 + x)(3 + x) = (x + -4)(x + 5)

Multiply (1 + x) * (3 + x)
(1(3 + x) + x(3 + x)) = (x + -4)(x + 5)
((3 * 1 + x * 1) + x(3 + x)) = (x + -4)(x + 5)
((3 + 1x) + x(3 + x)) = (x + -4)(x + 5)
(3 + 1x + (3 * x + x * x)) = (x + -4)(x + 5)
(3 + 1x + (3x + x2)) = (x + -4)(x + 5)

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = (x + -4)(x + 5)

Reorder the terms:
3 + 4x + x2 = (-4 + x)(x + 5)

Reorder the terms:
3 + 4x + x2 = (-4 + x)(5 + x)

Multiply (-4 + x) * (5 + x)
3 + 4x + x2 = (-4(5 + x) + x(5 + x))
3 + 4x + x2 = ((5 * -4 + x * -4) + x(5 + x))
3 + 4x + x2 = ((-20 + -4x) + x(5 + x))
3 + 4x + x2 = (-20 + -4x + (5 * x + x * x))
3 + 4x + x2 = (-20 + -4x + (5x + x2))

Combine like terms: -4x + 5x = 1x
3 + 4x + x2 = (-20 + 1x + x2)

Add '-1x2' to each side of the equation.
3 + 4x + x2 + -1x2 = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x + 0 = -20 + 1x + x2 + -1x2
3 + 4x = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x = -20 + 1x + 0
3 + 4x = -20 + 1x

Solving
3 + 4x = -20 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
3 + 4x + -1x = -20 + 1x + -1x

Combine like terms: 4x + -1x = 3x
3 + 3x = -20 + 1x + -1x

Combine like terms: 1x + -1x = 0
3 + 3x = -20 + 0
3 + 3x = -20

Add '-3' to each side of the equation.
3 + -3 + 3x = -20 + -3

Combine like terms: 3 + -3 = 0
0 + 3x = -20 + -3
3x = -20 + -3

Combine like terms: -20 + -3 = -23
3x = -23

Divide each side by '3'.
x = -7.666666667

Simplifying
x = -7.666666667