ax^2+(x-1)=(x+1)a

Solution for ax^2+(x-1)=(x+1)a equation:

Simplifying
ax2 + (x + -1) = (x + 1) * a

Reorder the terms:
ax2 + (-1 + x) = (x + 1) * a

Remove parenthesis around (-1 + x)
ax2 + -1 + x = (x + 1) * a

Reorder the terms:
-1 + ax2 + x = (x + 1) * a

Reorder the terms:
-1 + ax2 + x = (1 + x) * a

Reorder the terms for easier multiplication:
-1 + ax2 + x = a(1 + x)
-1 + ax2 + x = (1 * a + x * a)
-1 + ax2 + x = (1a + ax)

Solving
-1 + ax2 + x = 1a + ax

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
-1 + ax2 + -1a + x = 1a + -1a + ax

Reorder the terms:
-1 + -1a + ax2 + x = 1a + -1a + ax

Combine like terms: 1a + -1a = 0
-1 + -1a + ax2 + x = 0 + ax
-1 + -1a + ax2 + x = ax

Add '-1ax' to each side of the equation.
-1 + -1a + ax2 + -1ax + x = ax + -1ax

Reorder the terms:
-1 + -1a + -1ax + ax2 + x = ax + -1ax

Combine like terms: ax + -1ax = 0
-1 + -1a + -1ax + ax2 + x = 0

Add '1' to each side of the equation.
-1 + -1a + -1ax + ax2 + 1 + x = 0 + 1

Reorder the terms:
-1 + 1 + -1a + -1ax + ax2 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1a + -1ax + ax2 + x = 0 + 1
-1a + -1ax + ax2 + x = 0 + 1

Combine like terms: 0 + 1 = 1
-1a + -1ax + ax2 + x = 1

Add '-1x' to each side of the equation.
-1a + -1ax + ax2 + x + -1x = 1 + -1x

Combine like terms: x + -1x = 0
-1a + -1ax + ax2 + 0 = 1 + -1x
-1a + -1ax + ax2 = 1 + -1x

Reorder the terms:
-1 + -1a + -1ax + ax2 + x = 1 + -1x + -1 + x

Reorder the terms:
-1 + -1a + -1ax + ax2 + x = 1 + -1 + -1x + x

Combine like terms: 1 + -1 = 0
-1 + -1a + -1ax + ax2 + x = 0 + -1x + x
-1 + -1a + -1ax + ax2 + x = -1x + x

Combine like terms: -1x + x = 0
-1 + -1a + -1ax + ax2 + x = 0

The solution to this equation could not be determined.