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

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


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

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

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

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

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) = (x + -2)(x + -3)

Reorder the terms:
12 + 7x + x2 = (-2 + x)(x + -3)

Reorder the terms:
12 + 7x + x2 = (-2 + x)(-3 + x)

Multiply (-2 + x) * (-3 + x)
12 + 7x + x2 = (-2(-3 + x) + x(-3 + x))
12 + 7x + x2 = ((-3 * -2 + x * -2) + x(-3 + x))
12 + 7x + x2 = ((6 + -2x) + x(-3 + x))
12 + 7x + x2 = (6 + -2x + (-3 * x + x * x))
12 + 7x + x2 = (6 + -2x + (-3x + x2))

Combine like terms: -2x + -3x = -5x
12 + 7x + x2 = (6 + -5x + x2)

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

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

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

Solving
12 + 7x = 6 + -5x

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
x = -0.5

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