(x^2+ax+2b)+(x^2-2bx+3a)=cx^2-7x+3

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Solution for (x^2+ax+2b)+(x^2-2bx+3a)=cx^2-7x+3 equation: 


Simplifying
(x2 + ax + 2b) + (x2 + -2bx + 3a) = cx2 + -7x + 3

Reorder the terms:
(ax + 2b + x2) + (x2 + -2bx + 3a) = cx2 + -7x + 3

Remove parenthesis around (ax + 2b + x2)
ax + 2b + x2 + (x2 + -2bx + 3a) = cx2 + -7x + 3

Reorder the terms:
ax + 2b + x2 + (3a + -2bx + x2) = cx2 + -7x + 3

Remove parenthesis around (3a + -2bx + x2)
ax + 2b + x2 + 3a + -2bx + x2 = cx2 + -7x + 3

Reorder the terms:
3a + ax + 2b + -2bx + x2 + x2 = cx2 + -7x + 3

Combine like terms: x2 + x2 = 2x2
3a + ax + 2b + -2bx + 2x2 = cx2 + -7x + 3

Reorder the terms:
3a + ax + 2b + -2bx + 2x2 = 3 + cx2 + -7x

Solving
3a + ax + 2b + -2bx + 2x2 = 3 + cx2 + -7x

Solving for variable 'a'.

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

Add '-2b' to each side of the equation.
3a + ax + 2b + -2bx + -2b + 2x2 = 3 + cx2 + -2b + -7x

Reorder the terms:
3a + ax + 2b + -2b + -2bx + 2x2 = 3 + cx2 + -2b + -7x

Combine like terms: 2b + -2b = 0
3a + ax + 0 + -2bx + 2x2 = 3 + cx2 + -2b + -7x
3a + ax + -2bx + 2x2 = 3 + cx2 + -2b + -7x

Reorder the terms:
3a + ax + -2bx + 2x2 = 3 + -2b + cx2 + -7x

Add '2bx' to each side of the equation.
3a + ax + -2bx + 2bx + 2x2 = 3 + -2b + cx2 + 2bx + -7x

Combine like terms: -2bx + 2bx = 0
3a + ax + 0 + 2x2 = 3 + -2b + cx2 + 2bx + -7x
3a + ax + 2x2 = 3 + -2b + cx2 + 2bx + -7x

Reorder the terms:
3a + ax + 2x2 = 3 + -2b + 2bx + cx2 + -7x

Add '-2x2' to each side of the equation.
3a + ax + 2x2 + -2x2 = 3 + -2b + 2bx + cx2 + -7x + -2x2

Combine like terms: 2x2 + -2x2 = 0
3a + ax + 0 = 3 + -2b + 2bx + cx2 + -7x + -2x2
3a + ax = 3 + -2b + 2bx + cx2 + -7x + -2x2

Reorder the terms:
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 3 + -2b + 2bx + cx2 + -7x + -2x2 + -3 + 2b + -2bx + -1cx2 + 7x + 2x2

Reorder the terms:
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 3 + -3 + -2b + 2b + 2bx + -2bx + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2

Combine like terms: 3 + -3 = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0 + -2b + 2b + 2bx + -2bx + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = -2b + 2b + 2bx + -2bx + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2

Combine like terms: -2b + 2b = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0 + 2bx + -2bx + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 2bx + -2bx + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2

Combine like terms: 2bx + -2bx = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0 + cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = cx2 + -1cx2 + -7x + 7x + -2x2 + 2x2

Combine like terms: cx2 + -1cx2 = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0 + -7x + 7x + -2x2 + 2x2
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = -7x + 7x + -2x2 + 2x2

Combine like terms: -7x + 7x = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0 + -2x2 + 2x2
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-3 + 3a + ax + 2b + -2bx + -1cx2 + 7x + 2x2 = 0

The solution to this equation could not be determined.

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