(7x^2+4x-7)-(nx^2-8)=2x^2+4x+1

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Solution for (7x^2+4x-7)-(nx^2-8)=2x^2+4x+1 equation:


Simplifying
(7x2 + 4x + -7) + -1(nx2 + -8) = 2x2 + 4x + 1

Reorder the terms:
(-7 + 4x + 7x2) + -1(nx2 + -8) = 2x2 + 4x + 1

Remove parenthesis around (-7 + 4x + 7x2)
-7 + 4x + 7x2 + -1(nx2 + -8) = 2x2 + 4x + 1

Reorder the terms:
-7 + 4x + 7x2 + -1(-8 + nx2) = 2x2 + 4x + 1
-7 + 4x + 7x2 + (-8 * -1 + nx2 * -1) = 2x2 + 4x + 1
-7 + 4x + 7x2 + (8 + -1nx2) = 2x2 + 4x + 1

Reorder the terms:
-7 + 8 + -1nx2 + 4x + 7x2 = 2x2 + 4x + 1

Combine like terms: -7 + 8 = 1
1 + -1nx2 + 4x + 7x2 = 2x2 + 4x + 1

Reorder the terms:
1 + -1nx2 + 4x + 7x2 = 1 + 4x + 2x2

Add '-1' to each side of the equation.
1 + -1nx2 + 4x + -1 + 7x2 = 1 + 4x + -1 + 2x2

Reorder the terms:
1 + -1 + -1nx2 + 4x + 7x2 = 1 + 4x + -1 + 2x2

Combine like terms: 1 + -1 = 0
0 + -1nx2 + 4x + 7x2 = 1 + 4x + -1 + 2x2
-1nx2 + 4x + 7x2 = 1 + 4x + -1 + 2x2

Reorder the terms:
-1nx2 + 4x + 7x2 = 1 + -1 + 4x + 2x2

Combine like terms: 1 + -1 = 0
-1nx2 + 4x + 7x2 = 0 + 4x + 2x2
-1nx2 + 4x + 7x2 = 4x + 2x2

Add '-4x' to each side of the equation.
-1nx2 + 4x + -4x + 7x2 = 4x + -4x + 2x2

Combine like terms: 4x + -4x = 0
-1nx2 + 0 + 7x2 = 4x + -4x + 2x2
-1nx2 + 7x2 = 4x + -4x + 2x2

Combine like terms: 4x + -4x = 0
-1nx2 + 7x2 = 0 + 2x2
-1nx2 + 7x2 = 2x2

Solving
-1nx2 + 7x2 = 2x2

Solving for variable 'n'.

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

Add '-7x2' to each side of the equation.
-1nx2 + 7x2 + -7x2 = 2x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-1nx2 + 0 = 2x2 + -7x2
-1nx2 = 2x2 + -7x2

Combine like terms: 2x2 + -7x2 = -5x2
-1nx2 = -5x2

Divide each side by '-1x2'.
n = 5

Simplifying
n = 5

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