(a-b)(x^2-5)+(b-a)(3x+5)=

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Solution for (a-b)(x^2-5)+(b-a)(3x+5)= equation: 


Simplifying
(a + -1b)(x2 + -5) + (b + -1a)(3x + 5) = 0

Reorder the terms:
(a + -1b)(-5 + x2) + (b + -1a)(3x + 5) = 0

Multiply (a + -1b) * (-5 + x2)
(a(-5 + x2) + -1b * (-5 + x2)) + (b + -1a)(3x + 5) = 0
((-5 * a + x2 * a) + -1b * (-5 + x2)) + (b + -1a)(3x + 5) = 0
((-5a + ax2) + -1b * (-5 + x2)) + (b + -1a)(3x + 5) = 0
(-5a + ax2 + (-5 * -1b + x2 * -1b)) + (b + -1a)(3x + 5) = 0
(-5a + ax2 + (5b + -1bx2)) + (b + -1a)(3x + 5) = 0
(-5a + ax2 + 5b + -1bx2) + (b + -1a)(3x + 5) = 0

Reorder the terms:
-5a + ax2 + 5b + -1bx2 + (-1a + b)(3x + 5) = 0

Reorder the terms:
-5a + ax2 + 5b + -1bx2 + (-1a + b)(5 + 3x) = 0

Multiply (-1a + b) * (5 + 3x)
-5a + ax2 + 5b + -1bx2 + (-1a * (5 + 3x) + b(5 + 3x)) = 0
-5a + ax2 + 5b + -1bx2 + ((5 * -1a + 3x * -1a) + b(5 + 3x)) = 0
-5a + ax2 + 5b + -1bx2 + ((-5a + -3ax) + b(5 + 3x)) = 0
-5a + ax2 + 5b + -1bx2 + (-5a + -3ax + (5 * b + 3x * b)) = 0
-5a + ax2 + 5b + -1bx2 + (-5a + -3ax + (5b + 3bx)) = 0
-5a + ax2 + 5b + -1bx2 + (-5a + -3ax + 5b + 3bx) = 0

Reorder the terms:
-5a + -5a + -3ax + ax2 + 5b + 5b + 3bx + -1bx2 = 0

Combine like terms: -5a + -5a = -10a
-10a + -3ax + ax2 + 5b + 5b + 3bx + -1bx2 = 0

Combine like terms: 5b + 5b = 10b
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = 0

Solving
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = 0

Solving for variable 'a'.

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

Add '-10b' to each side of the equation.
-10a + -3ax + ax2 + 10b + 3bx + -10b + -1bx2 = 0 + -10b

Reorder the terms:
-10a + -3ax + ax2 + 10b + -10b + 3bx + -1bx2 = 0 + -10b

Combine like terms: 10b + -10b = 0
-10a + -3ax + ax2 + 0 + 3bx + -1bx2 = 0 + -10b
-10a + -3ax + ax2 + 3bx + -1bx2 = 0 + -10b
Remove the zero:
-10a + -3ax + ax2 + 3bx + -1bx2 = -10b

Add '-3bx' to each side of the equation.
-10a + -3ax + ax2 + 3bx + -3bx + -1bx2 = -10b + -3bx

Combine like terms: 3bx + -3bx = 0
-10a + -3ax + ax2 + 0 + -1bx2 = -10b + -3bx
-10a + -3ax + ax2 + -1bx2 = -10b + -3bx

Add 'bx2' to each side of the equation.
-10a + -3ax + ax2 + -1bx2 + bx2 = -10b + -3bx + bx2

Combine like terms: -1bx2 + bx2 = 0
-10a + -3ax + ax2 + 0 = -10b + -3bx + bx2
-10a + -3ax + ax2 = -10b + -3bx + bx2

Reorder the terms:
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = -10b + 10b + -3bx + 3bx + bx2 + -1bx2

Combine like terms: -10b + 10b = 0
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = 0 + -3bx + 3bx + bx2 + -1bx2
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = -3bx + 3bx + bx2 + -1bx2

Combine like terms: -3bx + 3bx = 0
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = 0 + bx2 + -1bx2
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = bx2 + -1bx2

Combine like terms: bx2 + -1bx2 = 0
-10a + -3ax + ax2 + 10b + 3bx + -1bx2 = 0

The solution to this equation could not be determined.

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