(6X+1)(6X-1)-(9X+5)(4X-3)=0

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Solution for (6X+1)(6X-1)-(9X+5)(4X-3)=0 equation: 


Simplifying
(6X + 1)(6X + -1) + -1(9X + 5)(4X + -3) = 0

Reorder the terms:
(1 + 6X)(6X + -1) + -1(9X + 5)(4X + -3) = 0

Reorder the terms:
(1 + 6X)(-1 + 6X) + -1(9X + 5)(4X + -3) = 0

Multiply (1 + 6X) * (-1 + 6X)
(1(-1 + 6X) + 6X * (-1 + 6X)) + -1(9X + 5)(4X + -3) = 0
((-1 * 1 + 6X * 1) + 6X * (-1 + 6X)) + -1(9X + 5)(4X + -3) = 0
((-1 + 6X) + 6X * (-1 + 6X)) + -1(9X + 5)(4X + -3) = 0
(-1 + 6X + (-1 * 6X + 6X * 6X)) + -1(9X + 5)(4X + -3) = 0
(-1 + 6X + (-6X + 36X2)) + -1(9X + 5)(4X + -3) = 0

Combine like terms: 6X + -6X = 0
(-1 + 0 + 36X2) + -1(9X + 5)(4X + -3) = 0
(-1 + 36X2) + -1(9X + 5)(4X + -3) = 0

Reorder the terms:
-1 + 36X2 + -1(5 + 9X)(4X + -3) = 0

Reorder the terms:
-1 + 36X2 + -1(5 + 9X)(-3 + 4X) = 0

Multiply (5 + 9X) * (-3 + 4X)
-1 + 36X2 + -1(5(-3 + 4X) + 9X * (-3 + 4X)) = 0
-1 + 36X2 + -1((-3 * 5 + 4X * 5) + 9X * (-3 + 4X)) = 0
-1 + 36X2 + -1((-15 + 20X) + 9X * (-3 + 4X)) = 0
-1 + 36X2 + -1(-15 + 20X + (-3 * 9X + 4X * 9X)) = 0
-1 + 36X2 + -1(-15 + 20X + (-27X + 36X2)) = 0

Combine like terms: 20X + -27X = -7X
-1 + 36X2 + -1(-15 + -7X + 36X2) = 0
-1 + 36X2 + (-15 * -1 + -7X * -1 + 36X2 * -1) = 0
-1 + 36X2 + (15 + 7X + -36X2) = 0

Reorder the terms:
-1 + 15 + 7X + 36X2 + -36X2 = 0

Combine like terms: -1 + 15 = 14
14 + 7X + 36X2 + -36X2 = 0

Combine like terms: 36X2 + -36X2 = 0
14 + 7X + 0 = 0
14 + 7X = 0

Solving
14 + 7X = 0

Solving for variable 'X'.

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

Add '-14' to each side of the equation.
14 + -14 + 7X = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 7X = 0 + -14
7X = 0 + -14

Combine like terms: 0 + -14 = -14
7X = -14

Divide each side by '7'.
X = -2

Simplifying
X = -2

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