(4a+3)x(3b+4)=(6a+1)x(2b-3)

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Solution for (4a+3)x(3b+4)=(6a+1)x(2b-3) equation:


Simplifying
(4a + 3) * x(3b + 4) = (6a + 1) * x(2b + -3)

Reorder the terms:
(3 + 4a) * x(3b + 4) = (6a + 1) * x(2b + -3)

Reorder the terms:
(3 + 4a) * x(4 + 3b) = (6a + 1) * x(2b + -3)

Reorder the terms for easier multiplication:
x(3 + 4a)(4 + 3b) = (6a + 1) * x(2b + -3)

Multiply (3 + 4a) * (4 + 3b)
x(3(4 + 3b) + 4a * (4 + 3b)) = (6a + 1) * x(2b + -3)
x((4 * 3 + 3b * 3) + 4a * (4 + 3b)) = (6a + 1) * x(2b + -3)
x((12 + 9b) + 4a * (4 + 3b)) = (6a + 1) * x(2b + -3)
x(12 + 9b + (4 * 4a + 3b * 4a)) = (6a + 1) * x(2b + -3)
x(12 + 9b + (16a + 12ab)) = (6a + 1) * x(2b + -3)

Reorder the terms:
x(12 + 16a + 12ab + 9b) = (6a + 1) * x(2b + -3)
x(12 + 16a + 12ab + 9b) = (6a + 1) * x(2b + -3)
(12 * x + 16a * x + 12ab * x + 9b * x) = (6a + 1) * x(2b + -3)

Reorder the terms:
(12abx + 16ax + 9bx + 12x) = (6a + 1) * x(2b + -3)
(12abx + 16ax + 9bx + 12x) = (6a + 1) * x(2b + -3)

Reorder the terms:
12abx + 16ax + 9bx + 12x = (1 + 6a) * x(2b + -3)

Reorder the terms:
12abx + 16ax + 9bx + 12x = (1 + 6a) * x(-3 + 2b)

Reorder the terms for easier multiplication:
12abx + 16ax + 9bx + 12x = x(1 + 6a)(-3 + 2b)

Multiply (1 + 6a) * (-3 + 2b)
12abx + 16ax + 9bx + 12x = x(1(-3 + 2b) + 6a * (-3 + 2b))
12abx + 16ax + 9bx + 12x = x((-3 * 1 + 2b * 1) + 6a * (-3 + 2b))
12abx + 16ax + 9bx + 12x = x((-3 + 2b) + 6a * (-3 + 2b))
12abx + 16ax + 9bx + 12x = x(-3 + 2b + (-3 * 6a + 2b * 6a))
12abx + 16ax + 9bx + 12x = x(-3 + 2b + (-18a + 12ab))

Reorder the terms:
12abx + 16ax + 9bx + 12x = x(-3 + -18a + 12ab + 2b)
12abx + 16ax + 9bx + 12x = x(-3 + -18a + 12ab + 2b)
12abx + 16ax + 9bx + 12x = (-3 * x + -18a * x + 12ab * x + 2b * x)

Reorder the terms:
12abx + 16ax + 9bx + 12x = (12abx + -18ax + 2bx + -3x)
12abx + 16ax + 9bx + 12x = (12abx + -18ax + 2bx + -3x)

Add '-12abx' to each side of the equation.
12abx + 16ax + 9bx + -12abx + 12x = 12abx + -18ax + 2bx + -12abx + -3x

Reorder the terms:
12abx + -12abx + 16ax + 9bx + 12x = 12abx + -18ax + 2bx + -12abx + -3x

Combine like terms: 12abx + -12abx = 0
0 + 16ax + 9bx + 12x = 12abx + -18ax + 2bx + -12abx + -3x
16ax + 9bx + 12x = 12abx + -18ax + 2bx + -12abx + -3x

Reorder the terms:
16ax + 9bx + 12x = 12abx + -12abx + -18ax + 2bx + -3x

Combine like terms: 12abx + -12abx = 0
16ax + 9bx + 12x = 0 + -18ax + 2bx + -3x
16ax + 9bx + 12x = -18ax + 2bx + -3x

Solving
16ax + 9bx + 12x = -18ax + 2bx + -3x

Solving for variable 'a'.

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

Add '18ax' to each side of the equation.
16ax + 9bx + 18ax + 12x = -18ax + 2bx + 18ax + -3x

Reorder the terms:
16ax + 18ax + 9bx + 12x = -18ax + 2bx + 18ax + -3x

Combine like terms: 16ax + 18ax = 34ax
34ax + 9bx + 12x = -18ax + 2bx + 18ax + -3x

Reorder the terms:
34ax + 9bx + 12x = -18ax + 18ax + 2bx + -3x

Combine like terms: -18ax + 18ax = 0
34ax + 9bx + 12x = 0 + 2bx + -3x
34ax + 9bx + 12x = 2bx + -3x

Add '-9bx' to each side of the equation.
34ax + 9bx + -9bx + 12x = 2bx + -9bx + -3x

Combine like terms: 9bx + -9bx = 0
34ax + 0 + 12x = 2bx + -9bx + -3x
34ax + 12x = 2bx + -9bx + -3x

Combine like terms: 2bx + -9bx = -7bx
34ax + 12x = -7bx + -3x

Add '-12x' to each side of the equation.
34ax + 12x + -12x = -7bx + -3x + -12x

Combine like terms: 12x + -12x = 0
34ax + 0 = -7bx + -3x + -12x
34ax = -7bx + -3x + -12x

Combine like terms: -3x + -12x = -15x
34ax = -7bx + -15x

Divide each side by '34x'.
a = -0.2058823529b + -0.4411764706

Simplifying
a = -0.2058823529b + -0.4411764706

Reorder the terms:
a = -0.4411764706 + -0.2058823529b

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