(X-5)(X-7)-9=(X-6)(X+6)

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Solution for (X-5)(X-7)-9=(X-6)(X+6) equation: 


Simplifying
(X + -5)(X + -7) + -9 = (X + -6)(X + 6)

Reorder the terms:
(-5 + X)(X + -7) + -9 = (X + -6)(X + 6)

Reorder the terms:
(-5 + X)(-7 + X) + -9 = (X + -6)(X + 6)

Multiply (-5 + X) * (-7 + X)
(-5(-7 + X) + X(-7 + X)) + -9 = (X + -6)(X + 6)
((-7 * -5 + X * -5) + X(-7 + X)) + -9 = (X + -6)(X + 6)
((35 + -5X) + X(-7 + X)) + -9 = (X + -6)(X + 6)
(35 + -5X + (-7 * X + X * X)) + -9 = (X + -6)(X + 6)
(35 + -5X + (-7X + X2)) + -9 = (X + -6)(X + 6)

Combine like terms: -5X + -7X = -12X
(35 + -12X + X2) + -9 = (X + -6)(X + 6)

Reorder the terms:
35 + -9 + -12X + X2 = (X + -6)(X + 6)

Combine like terms: 35 + -9 = 26
26 + -12X + X2 = (X + -6)(X + 6)

Reorder the terms:
26 + -12X + X2 = (-6 + X)(X + 6)

Reorder the terms:
26 + -12X + X2 = (-6 + X)(6 + X)

Multiply (-6 + X) * (6 + X)
26 + -12X + X2 = (-6(6 + X) + X(6 + X))
26 + -12X + X2 = ((6 * -6 + X * -6) + X(6 + X))
26 + -12X + X2 = ((-36 + -6X) + X(6 + X))
26 + -12X + X2 = (-36 + -6X + (6 * X + X * X))
26 + -12X + X2 = (-36 + -6X + (6X + X2))

Combine like terms: -6X + 6X = 0
26 + -12X + X2 = (-36 + 0 + X2)
26 + -12X + X2 = (-36 + X2)

Add '-1X2' to each side of the equation.
26 + -12X + X2 + -1X2 = -36 + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
26 + -12X + 0 = -36 + X2 + -1X2
26 + -12X = -36 + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
26 + -12X = -36 + 0
26 + -12X = -36

Solving
26 + -12X = -36

Solving for variable 'X'.

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

Add '-26' to each side of the equation.
26 + -26 + -12X = -36 + -26

Combine like terms: 26 + -26 = 0
0 + -12X = -36 + -26
-12X = -36 + -26

Combine like terms: -36 + -26 = -62
-12X = -62

Divide each side by '-12'.
X = 5.166666667

Simplifying
X = 5.166666667

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