(x-3)(x+2)=(x-4)(x+1)-(x+1)(x+2)

Solution for (x-3)(x+2)=(x-4)(x+1)-(x+1)(x+2) equation:

Simplifying
(x + -3)(x + 2) = (x + -4)(x + 1) + -1(x + 1)(x + 2)

Reorder the terms:
(-3 + x)(x + 2) = (x + -4)(x + 1) + -1(x + 1)(x + 2)

Reorder the terms:
(-3 + x)(2 + x) = (x + -4)(x + 1) + -1(x + 1)(x + 2)

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = (x + -4)(x + 1) + -1(x + 1)(x + 2)
((2 * -3 + x * -3) + x(2 + x)) = (x + -4)(x + 1) + -1(x + 1)(x + 2)
((-6 + -3x) + x(2 + x)) = (x + -4)(x + 1) + -1(x + 1)(x + 2)
(-6 + -3x + (2 * x + x * x)) = (x + -4)(x + 1) + -1(x + 1)(x + 2)
(-6 + -3x + (2x + x2)) = (x + -4)(x + 1) + -1(x + 1)(x + 2)

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = (x + -4)(x + 1) + -1(x + 1)(x + 2)

Reorder the terms:
-6 + -1x + x2 = (-4 + x)(x + 1) + -1(x + 1)(x + 2)

Reorder the terms:
-6 + -1x + x2 = (-4 + x)(1 + x) + -1(x + 1)(x + 2)

Multiply (-4 + x) * (1 + x)
-6 + -1x + x2 = (-4(1 + x) + x(1 + x)) + -1(x + 1)(x + 2)
-6 + -1x + x2 = ((1 * -4 + x * -4) + x(1 + x)) + -1(x + 1)(x + 2)
-6 + -1x + x2 = ((-4 + -4x) + x(1 + x)) + -1(x + 1)(x + 2)
-6 + -1x + x2 = (-4 + -4x + (1 * x + x * x)) + -1(x + 1)(x + 2)
-6 + -1x + x2 = (-4 + -4x + (1x + x2)) + -1(x + 1)(x + 2)

Combine like terms: -4x + 1x = -3x
-6 + -1x + x2 = (-4 + -3x + x2) + -1(x + 1)(x + 2)

Reorder the terms:
-6 + -1x + x2 = -4 + -3x + x2 + -1(1 + x)(x + 2)

Reorder the terms:
-6 + -1x + x2 = -4 + -3x + x2 + -1(1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
-6 + -1x + x2 = -4 + -3x + x2 + -1(1(2 + x) + x(2 + x))
-6 + -1x + x2 = -4 + -3x + x2 + -1((2 * 1 + x * 1) + x(2 + x))
-6 + -1x + x2 = -4 + -3x + x2 + -1((2 + 1x) + x(2 + x))
-6 + -1x + x2 = -4 + -3x + x2 + -1(2 + 1x + (2 * x + x * x))
-6 + -1x + x2 = -4 + -3x + x2 + -1(2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
-6 + -1x + x2 = -4 + -3x + x2 + -1(2 + 3x + x2)
-6 + -1x + x2 = -4 + -3x + x2 + (2 * -1 + 3x * -1 + x2 * -1)
-6 + -1x + x2 = -4 + -3x + x2 + (-2 + -3x + -1x2)

Reorder the terms:
-6 + -1x + x2 = -4 + -2 + -3x + -3x + x2 + -1x2

Combine like terms: -4 + -2 = -6
-6 + -1x + x2 = -6 + -3x + -3x + x2 + -1x2

Combine like terms: -3x + -3x = -6x
-6 + -1x + x2 = -6 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -1x + x2 = -6 + -6x + 0
-6 + -1x + x2 = -6 + -6x

Add '6' to each side of the equation.
-6 + -1x + 6 + x2 = -6 + 6 + -6x

Reorder the terms:
-6 + 6 + -1x + x2 = -6 + 6 + -6x

Combine like terms: -6 + 6 = 0
0 + -1x + x2 = -6 + 6 + -6x
-1x + x2 = -6 + 6 + -6x

Combine like terms: -6 + 6 = 0
-1x + x2 = 0 + -6x
-1x + x2 = -6x

Solving
-1x + x2 = -6x

Solving for variable 'x'.

Reorder the terms:
-1x + 6x + x2 = -6x + 6x

Combine like terms: -1x + 6x = 5x
5x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
5x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}