8a^2-45ab-18b^2=(a-6b)(8a-3b)

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Solution for 8a^2-45ab-18b^2=(a-6b)(8a-3b) equation: 


Simplifying
8a2 + -45ab + -18b2 = (a + -6b)(8a + -3b)

Reorder the terms:
-45ab + 8a2 + -18b2 = (a + -6b)(8a + -3b)

Multiply (a + -6b) * (8a + -3b)
-45ab + 8a2 + -18b2 = (a(8a + -3b) + -6b * (8a + -3b))
-45ab + 8a2 + -18b2 = ((8a * a + -3b * a) + -6b * (8a + -3b))

Reorder the terms:
-45ab + 8a2 + -18b2 = ((-3ab + 8a2) + -6b * (8a + -3b))
-45ab + 8a2 + -18b2 = ((-3ab + 8a2) + -6b * (8a + -3b))
-45ab + 8a2 + -18b2 = (-3ab + 8a2 + (8a * -6b + -3b * -6b))
-45ab + 8a2 + -18b2 = (-3ab + 8a2 + (-48ab + 18b2))

Reorder the terms:
-45ab + 8a2 + -18b2 = (-3ab + -48ab + 8a2 + 18b2)

Combine like terms: -3ab + -48ab = -51ab
-45ab + 8a2 + -18b2 = (-51ab + 8a2 + 18b2)

Add '-8a2' to each side of the equation.
-45ab + 8a2 + -8a2 + -18b2 = -51ab + 8a2 + -8a2 + 18b2

Combine like terms: 8a2 + -8a2 = 0
-45ab + 0 + -18b2 = -51ab + 8a2 + -8a2 + 18b2
-45ab + -18b2 = -51ab + 8a2 + -8a2 + 18b2

Combine like terms: 8a2 + -8a2 = 0
-45ab + -18b2 = -51ab + 0 + 18b2
-45ab + -18b2 = -51ab + 18b2

Solving
-45ab + -18b2 = -51ab + 18b2

Solving for variable 'a'.

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

Add '51ab' to each side of the equation.
-45ab + 51ab + -18b2 = -51ab + 51ab + 18b2

Combine like terms: -45ab + 51ab = 6ab
6ab + -18b2 = -51ab + 51ab + 18b2

Combine like terms: -51ab + 51ab = 0
6ab + -18b2 = 0 + 18b2
6ab + -18b2 = 18b2

Add '18b2' to each side of the equation.
6ab + -18b2 + 18b2 = 18b2 + 18b2

Combine like terms: -18b2 + 18b2 = 0
6ab + 0 = 18b2 + 18b2
6ab = 18b2 + 18b2

Combine like terms: 18b2 + 18b2 = 36b2
6ab = 36b2

Divide each side by '6b'.
a = 6b

Simplifying
a = 6b

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