2x+5=(x^2+m^2)-(x^2-n^2)

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Solution for 2x+5=(x^2+m^2)-(x^2-n^2) equation:


Simplifying
2x + 5 = (x2 + m2) + -1(x2 + -1n2)

Reorder the terms:
5 + 2x = (x2 + m2) + -1(x2 + -1n2)

Reorder the terms:
5 + 2x = (m2 + x2) + -1(x2 + -1n2)

Remove parenthesis around (m2 + x2)
5 + 2x = m2 + x2 + -1(x2 + -1n2)

Reorder the terms:
5 + 2x = m2 + x2 + -1(-1n2 + x2)
5 + 2x = m2 + x2 + (-1n2 * -1 + x2 * -1)
5 + 2x = m2 + x2 + (1n2 + -1x2)

Reorder the terms:
5 + 2x = m2 + 1n2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 2x = m2 + 1n2 + 0
5 + 2x = m2 + 1n2

Solving
5 + 2x = m2 + 1n2

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + 2x = m2 + -5 + 1n2

Combine like terms: 5 + -5 = 0
0 + 2x = m2 + -5 + 1n2
2x = m2 + -5 + 1n2

Reorder the terms:
2x = -5 + m2 + 1n2

Divide each side by '2'.
x = -2.5 + 0.5m2 + 0.5n2

Simplifying
x = -2.5 + 0.5m2 + 0.5n2

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