(6x-5a)(3a-4x)=(2b-3x)(8x+5b)

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Solution for (6x-5a)(3a-4x)=(2b-3x)(8x+5b) equation: 


Simplifying
(6x + -5a)(3a + -4x) = (2b + -3x)(8x + 5b)

Reorder the terms:
(-5a + 6x)(3a + -4x) = (2b + -3x)(8x + 5b)

Multiply (-5a + 6x) * (3a + -4x)
(-5a * (3a + -4x) + 6x * (3a + -4x)) = (2b + -3x)(8x + 5b)
((3a * -5a + -4x * -5a) + 6x * (3a + -4x)) = (2b + -3x)(8x + 5b)

Reorder the terms:
((20ax + -15a2) + 6x * (3a + -4x)) = (2b + -3x)(8x + 5b)
((20ax + -15a2) + 6x * (3a + -4x)) = (2b + -3x)(8x + 5b)
(20ax + -15a2 + (3a * 6x + -4x * 6x)) = (2b + -3x)(8x + 5b)
(20ax + -15a2 + (18ax + -24x2)) = (2b + -3x)(8x + 5b)

Reorder the terms:
(20ax + 18ax + -15a2 + -24x2) = (2b + -3x)(8x + 5b)

Combine like terms: 20ax + 18ax = 38ax
(38ax + -15a2 + -24x2) = (2b + -3x)(8x + 5b)

Reorder the terms:
38ax + -15a2 + -24x2 = (2b + -3x)(5b + 8x)

Multiply (2b + -3x) * (5b + 8x)
38ax + -15a2 + -24x2 = (2b * (5b + 8x) + -3x * (5b + 8x))
38ax + -15a2 + -24x2 = ((5b * 2b + 8x * 2b) + -3x * (5b + 8x))

Reorder the terms:
38ax + -15a2 + -24x2 = ((16bx + 10b2) + -3x * (5b + 8x))
38ax + -15a2 + -24x2 = ((16bx + 10b2) + -3x * (5b + 8x))
38ax + -15a2 + -24x2 = (16bx + 10b2 + (5b * -3x + 8x * -3x))
38ax + -15a2 + -24x2 = (16bx + 10b2 + (-15bx + -24x2))

Reorder the terms:
38ax + -15a2 + -24x2 = (16bx + -15bx + 10b2 + -24x2)

Combine like terms: 16bx + -15bx = 1bx
38ax + -15a2 + -24x2 = (1bx + 10b2 + -24x2)

Add '24x2' to each side of the equation.
38ax + -15a2 + -24x2 + 24x2 = 1bx + 10b2 + -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
38ax + -15a2 + 0 = 1bx + 10b2 + -24x2 + 24x2
38ax + -15a2 = 1bx + 10b2 + -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
38ax + -15a2 = 1bx + 10b2 + 0
38ax + -15a2 = 1bx + 10b2

Solving
38ax + -15a2 = 1bx + 10b2

Solving for variable 'a'.

Reorder the terms:
38ax + -15a2 + -1bx + -10b2 = 1bx + -1bx + 10b2 + -10b2

Combine like terms: 1bx + -1bx = 0
38ax + -15a2 + -1bx + -10b2 = 0 + 10b2 + -10b2
38ax + -15a2 + -1bx + -10b2 = 10b2 + -10b2

Combine like terms: 10b2 + -10b2 = 0
38ax + -15a2 + -1bx + -10b2 = 0

The solution to this equation could not be determined.

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