(z-1)(z-2)=(z-3)(z-4)

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


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

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

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

Multiply (-1 + z) * (-2 + z)
(-1(-2 + z) + z(-2 + z)) = (z + -3)(z + -4)
((-2 * -1 + z * -1) + z(-2 + z)) = (z + -3)(z + -4)
((2 + -1z) + z(-2 + z)) = (z + -3)(z + -4)
(2 + -1z + (-2 * z + z * z)) = (z + -3)(z + -4)
(2 + -1z + (-2z + z2)) = (z + -3)(z + -4)

Combine like terms: -1z + -2z = -3z
(2 + -3z + z2) = (z + -3)(z + -4)

Reorder the terms:
2 + -3z + z2 = (-3 + z)(z + -4)

Reorder the terms:
2 + -3z + z2 = (-3 + z)(-4 + z)

Multiply (-3 + z) * (-4 + z)
2 + -3z + z2 = (-3(-4 + z) + z(-4 + z))
2 + -3z + z2 = ((-4 * -3 + z * -3) + z(-4 + z))
2 + -3z + z2 = ((12 + -3z) + z(-4 + z))
2 + -3z + z2 = (12 + -3z + (-4 * z + z * z))
2 + -3z + z2 = (12 + -3z + (-4z + z2))

Combine like terms: -3z + -4z = -7z
2 + -3z + z2 = (12 + -7z + z2)

Add '-1z2' to each side of the equation.
2 + -3z + z2 + -1z2 = 12 + -7z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
2 + -3z + 0 = 12 + -7z + z2 + -1z2
2 + -3z = 12 + -7z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
2 + -3z = 12 + -7z + 0
2 + -3z = 12 + -7z

Solving
2 + -3z = 12 + -7z

Solving for variable 'z'.

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

Add '7z' to each side of the equation.
2 + -3z + 7z = 12 + -7z + 7z

Combine like terms: -3z + 7z = 4z
2 + 4z = 12 + -7z + 7z

Combine like terms: -7z + 7z = 0
2 + 4z = 12 + 0
2 + 4z = 12

Add '-2' to each side of the equation.
2 + -2 + 4z = 12 + -2

Combine like terms: 2 + -2 = 0
0 + 4z = 12 + -2
4z = 12 + -2

Combine like terms: 12 + -2 = 10
4z = 10

Divide each side by '4'.
z = 2.5

Simplifying
z = 2.5

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