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

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

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

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

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

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

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = (x + 3)(x + 4)

Reorder the terms:
6 + -5x + x2 = (3 + x)(x + 4)

Reorder the terms:
6 + -5x + x2 = (3 + x)(4 + x)

Multiply (3 + x) * (4 + x)
6 + -5x + x2 = (3(4 + x) + x(4 + x))
6 + -5x + x2 = ((4 * 3 + x * 3) + x(4 + x))
6 + -5x + x2 = ((12 + 3x) + x(4 + x))
6 + -5x + x2 = (12 + 3x + (4 * x + x * x))
6 + -5x + x2 = (12 + 3x + (4x + x2))

Combine like terms: 3x + 4x = 7x
6 + -5x + x2 = (12 + 7x + x2)

Add '-1x2' to each side of the equation.
6 + -5x + x2 + -1x2 = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x + 0 = 12 + 7x + x2 + -1x2
6 + -5x = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x = 12 + 7x + 0
6 + -5x = 12 + 7x

Solving
6 + -5x = 12 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
6 + -5x + -7x = 12 + 7x + -7x

Combine like terms: -5x + -7x = -12x
6 + -12x = 12 + 7x + -7x

Combine like terms: 7x + -7x = 0
6 + -12x = 12 + 0
6 + -12x = 12

Add '-6' to each side of the equation.
6 + -6 + -12x = 12 + -6

Combine like terms: 6 + -6 = 0
0 + -12x = 12 + -6
-12x = 12 + -6

Combine like terms: 12 + -6 = 6
-12x = 6

Divide each side by '-12'.
x = -0.5

Simplifying
x = -0.5