300000=n-(((100000*0.07)+((n-100000)*0.03))*0.9)

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Solution for 300000=n-(((100000*0.07)+((n-100000)*0.03))*0.9) equation: 


Simplifying
300000 = n + -1(((100000 * 0.07) + ((n + -100000) * 0.03)) * 0.9)

Multiply 100000 * 0.07
300000 = n + -1(((7000) + ((n + -100000) * 0.03)) * 0.9)
300000 = n + -1((7000 + ((n + -100000) * 0.03)) * 0.9)

Reorder the terms:
300000 = n + -1((7000 + ((-100000 + n) * 0.03)) * 0.9)

Reorder the terms for easier multiplication:
300000 = n + -1((7000 + (0.03(-100000 + n))) * 0.9)
300000 = n + -1((7000 + ((-100000 * 0.03 + n * 0.03))) * 0.9)
300000 = n + -1((7000 + ((-3000 + 0.03n))) * 0.9)
300000 = n + -1((7000 + (-3000 + 0.03n)) * 0.9)

Remove parenthesis around (-3000 + 0.03n)
300000 = n + -1((7000 + -3000 + 0.03n) * 0.9)

Combine like terms: 7000 + -3000 = 4000
300000 = n + -1((4000 + 0.03n) * 0.9)

Reorder the terms for easier multiplication:
300000 = n + -1(0.9(4000 + 0.03n))
300000 = n + -1((4000 * 0.9 + 0.03n * 0.9))
300000 = n + -1((3600 + 0.027n))
300000 = n + (3600 * -1 + 0.027n * -1)
300000 = n + (-3600 + -0.027n)

Reorder the terms:
300000 = -3600 + n + -0.027n

Combine like terms: n + -0.027n = 0.973n
300000 = -3600 + 0.973n

Solving
300000 = -3600 + 0.973n

Solving for variable 'n'.

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

Add '-0.973n' to each side of the equation.
300000 + -0.973n = -3600 + 0.973n + -0.973n

Combine like terms: 0.973n + -0.973n = 0.000
300000 + -0.973n = -3600 + 0.000
300000 + -0.973n = -3600

Add '-300000' to each side of the equation.
300000 + -300000 + -0.973n = -3600 + -300000

Combine like terms: 300000 + -300000 = 0
0 + -0.973n = -3600 + -300000
-0.973n = -3600 + -300000

Combine like terms: -3600 + -300000 = -303600
-0.973n = -303600

Divide each side by '-0.973'.
n = 312024.666

Simplifying
n = 312024.666

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