(4n+2)+(2n-3)(3n-2)=6n^2-9n+8

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Solution for (4n+2)+(2n-3)(3n-2)=6n^2-9n+8 equation:


Simplifying
(4n + 2) + (2n + -3)(3n + -2) = 6n2 + -9n + 8

Reorder the terms:
(2 + 4n) + (2n + -3)(3n + -2) = 6n2 + -9n + 8

Remove parenthesis around (2 + 4n)
2 + 4n + (2n + -3)(3n + -2) = 6n2 + -9n + 8

Reorder the terms:
2 + 4n + (-3 + 2n)(3n + -2) = 6n2 + -9n + 8

Reorder the terms:
2 + 4n + (-3 + 2n)(-2 + 3n) = 6n2 + -9n + 8

Multiply (-3 + 2n) * (-2 + 3n)
2 + 4n + (-3(-2 + 3n) + 2n * (-2 + 3n)) = 6n2 + -9n + 8
2 + 4n + ((-2 * -3 + 3n * -3) + 2n * (-2 + 3n)) = 6n2 + -9n + 8
2 + 4n + ((6 + -9n) + 2n * (-2 + 3n)) = 6n2 + -9n + 8
2 + 4n + (6 + -9n + (-2 * 2n + 3n * 2n)) = 6n2 + -9n + 8
2 + 4n + (6 + -9n + (-4n + 6n2)) = 6n2 + -9n + 8

Combine like terms: -9n + -4n = -13n
2 + 4n + (6 + -13n + 6n2) = 6n2 + -9n + 8

Reorder the terms:
2 + 6 + 4n + -13n + 6n2 = 6n2 + -9n + 8

Combine like terms: 2 + 6 = 8
8 + 4n + -13n + 6n2 = 6n2 + -9n + 8

Combine like terms: 4n + -13n = -9n
8 + -9n + 6n2 = 6n2 + -9n + 8

Reorder the terms:
8 + -9n + 6n2 = 8 + -9n + 6n2

Add '-8' to each side of the equation.
8 + -9n + -8 + 6n2 = 8 + -9n + -8 + 6n2

Reorder the terms:
8 + -8 + -9n + 6n2 = 8 + -9n + -8 + 6n2

Combine like terms: 8 + -8 = 0
0 + -9n + 6n2 = 8 + -9n + -8 + 6n2
-9n + 6n2 = 8 + -9n + -8 + 6n2

Reorder the terms:
-9n + 6n2 = 8 + -8 + -9n + 6n2

Combine like terms: 8 + -8 = 0
-9n + 6n2 = 0 + -9n + 6n2
-9n + 6n2 = -9n + 6n2

Add '9n' to each side of the equation.
-9n + 9n + 6n2 = -9n + 9n + 6n2

Combine like terms: -9n + 9n = 0
0 + 6n2 = -9n + 9n + 6n2
6n2 = -9n + 9n + 6n2

Combine like terms: -9n + 9n = 0
6n2 = 0 + 6n2
6n2 = 6n2

Add '-6n2' to each side of the equation.
6n2 + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
0 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

 

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