a(2x+3)-b(3x+4)=10x+20

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Solution for a(2x+3)-b(3x+4)=10x+20 equation: 


Simplifying
a(2x + 3) + -1b(3x + 4) = 10x + 20

Reorder the terms:
a(3 + 2x) + -1b(3x + 4) = 10x + 20
(3 * a + 2x * a) + -1b(3x + 4) = 10x + 20
(3a + 2ax) + -1b(3x + 4) = 10x + 20

Reorder the terms:
3a + 2ax + -1b(4 + 3x) = 10x + 20
3a + 2ax + (4 * -1b + 3x * -1b) = 10x + 20
3a + 2ax + (-4b + -3bx) = 10x + 20

Reorder the terms:
3a + 2ax + -4b + -3bx = 20 + 10x

Solving
3a + 2ax + -4b + -3bx = 20 + 10x

Solving for variable 'a'.

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

Add '4b' to each side of the equation.
3a + 2ax + -4b + 4b + -3bx = 20 + 4b + 10x

Combine like terms: -4b + 4b = 0
3a + 2ax + 0 + -3bx = 20 + 4b + 10x
3a + 2ax + -3bx = 20 + 4b + 10x

Add '3bx' to each side of the equation.
3a + 2ax + -3bx + 3bx = 20 + 4b + 3bx + 10x

Combine like terms: -3bx + 3bx = 0
3a + 2ax + 0 = 20 + 4b + 3bx + 10x
3a + 2ax = 20 + 4b + 3bx + 10x

Reorder the terms:
-20 + 3a + 2ax + -4b + -3bx + -10x = 20 + 4b + 3bx + 10x + -20 + -4b + -3bx + -10x

Reorder the terms:
-20 + 3a + 2ax + -4b + -3bx + -10x = 20 + -20 + 4b + -4b + 3bx + -3bx + 10x + -10x

Combine like terms: 20 + -20 = 0
-20 + 3a + 2ax + -4b + -3bx + -10x = 0 + 4b + -4b + 3bx + -3bx + 10x + -10x
-20 + 3a + 2ax + -4b + -3bx + -10x = 4b + -4b + 3bx + -3bx + 10x + -10x

Combine like terms: 4b + -4b = 0
-20 + 3a + 2ax + -4b + -3bx + -10x = 0 + 3bx + -3bx + 10x + -10x
-20 + 3a + 2ax + -4b + -3bx + -10x = 3bx + -3bx + 10x + -10x

Combine like terms: 3bx + -3bx = 0
-20 + 3a + 2ax + -4b + -3bx + -10x = 0 + 10x + -10x
-20 + 3a + 2ax + -4b + -3bx + -10x = 10x + -10x

Combine like terms: 10x + -10x = 0
-20 + 3a + 2ax + -4b + -3bx + -10x = 0

The solution to this equation could not be determined.

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