(a-1)x^2=2bx+7x^2

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Solution for (a-1)x^2=2bx+7x^2 equation: 


Simplifying
(a + -1) * x2 = 2bx + 7x2

Reorder the terms:
(-1 + a) * x2 = 2bx + 7x2

Reorder the terms for easier multiplication:
x2(-1 + a) = 2bx + 7x2
(-1 * x2 + a * x2) = 2bx + 7x2

Reorder the terms:
(ax2 + -1x2) = 2bx + 7x2
(ax2 + -1x2) = 2bx + 7x2

Solving
ax2 + -1x2 = 2bx + 7x2

Solving for variable 'a'.

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

Add 'x2' to each side of the equation.
ax2 + -1x2 + x2 = 2bx + 7x2 + x2

Combine like terms: -1x2 + x2 = 0
ax2 + 0 = 2bx + 7x2 + x2
ax2 = 2bx + 7x2 + x2

Combine like terms: 7x2 + x2 = 8x2
ax2 = 2bx + 8x2

Divide each side by 'x2'.
a = 2bx-1 + 8

Simplifying
a = 2bx-1 + 8

Reorder the terms:
a = 8 + 2bx-1

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