(x+1)(x+2)-(x+3)(x-4)=0

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Solution for (x+1)(x+2)-(x+3)(x-4)=0 equation: 


Simplifying
(x + 1)(x + 2) + -1(x + 3)(x + -4) = 0

Reorder the terms:
(1 + x)(x + 2) + -1(x + 3)(x + -4) = 0

Reorder the terms:
(1 + x)(2 + x) + -1(x + 3)(x + -4) = 0

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) + -1(x + 3)(x + -4) = 0
((2 * 1 + x * 1) + x(2 + x)) + -1(x + 3)(x + -4) = 0
((2 + 1x) + x(2 + x)) + -1(x + 3)(x + -4) = 0
(2 + 1x + (2 * x + x * x)) + -1(x + 3)(x + -4) = 0
(2 + 1x + (2x + x2)) + -1(x + 3)(x + -4) = 0

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) + -1(x + 3)(x + -4) = 0

Reorder the terms:
2 + 3x + x2 + -1(3 + x)(x + -4) = 0

Reorder the terms:
2 + 3x + x2 + -1(3 + x)(-4 + x) = 0

Multiply (3 + x) * (-4 + x)
2 + 3x + x2 + -1(3(-4 + x) + x(-4 + x)) = 0
2 + 3x + x2 + -1((-4 * 3 + x * 3) + x(-4 + x)) = 0
2 + 3x + x2 + -1((-12 + 3x) + x(-4 + x)) = 0
2 + 3x + x2 + -1(-12 + 3x + (-4 * x + x * x)) = 0
2 + 3x + x2 + -1(-12 + 3x + (-4x + x2)) = 0

Combine like terms: 3x + -4x = -1x
2 + 3x + x2 + -1(-12 + -1x + x2) = 0
2 + 3x + x2 + (-12 * -1 + -1x * -1 + x2 * -1) = 0
2 + 3x + x2 + (12 + 1x + -1x2) = 0

Reorder the terms:
2 + 12 + 3x + 1x + x2 + -1x2 = 0

Combine like terms: 2 + 12 = 14
14 + 3x + 1x + x2 + -1x2 = 0

Combine like terms: 3x + 1x = 4x
14 + 4x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
14 + 4x + 0 = 0
14 + 4x = 0

Solving
14 + 4x = 0

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + 4x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 4x = 0 + -14
4x = 0 + -14

Combine like terms: 0 + -14 = -14
4x = -14

Divide each side by '4'.
x = -3.5

Simplifying
x = -3.5

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