(ax-by)(ax-by)+11(ax-by)-60=(ax-by+15)(ax-by-4)

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Solution for (ax-by)(ax-by)+11(ax-by)-60=(ax-by+15)(ax-by-4) equation: 


Simplifying
(ax + -1by)(ax + -1by) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)

Multiply (ax + -1by) * (ax + -1by)
(ax(ax + -1by) + -1by * (ax + -1by)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)
((ax * ax + -1by * ax) + -1by * (ax + -1by)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)

Reorder the terms:
((-1abxy + a2x2) + -1by * (ax + -1by)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)
((-1abxy + a2x2) + -1by * (ax + -1by)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)
(-1abxy + a2x2 + (ax * -1by + -1by * -1by)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)
(-1abxy + a2x2 + (-1abxy + 1b2y2)) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)

Reorder the terms:
(-1abxy + -1abxy + a2x2 + 1b2y2) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)

Combine like terms: -1abxy + -1abxy = -2abxy
(-2abxy + a2x2 + 1b2y2) + 11(ax + -1by) + -60 = (ax + -1by + 15)(ax + -1by + -4)
-2abxy + a2x2 + 1b2y2 + (ax * 11 + -1by * 11) + -60 = (ax + -1by + 15)(ax + -1by + -4)
-2abxy + a2x2 + 1b2y2 + (11ax + -11by) + -60 = (ax + -1by + 15)(ax + -1by + -4)

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (ax + -1by + 15)(ax + -1by + -4)

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (15 + ax + -1by)(ax + -1by + -4)

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (15 + ax + -1by)(-4 + ax + -1by)

Multiply (15 + ax + -1by) * (-4 + ax + -1by)
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (15(-4 + ax + -1by) + ax(-4 + ax + -1by) + -1by * (-4 + ax + -1by))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = ((-4 * 15 + ax * 15 + -1by * 15) + ax(-4 + ax + -1by) + -1by * (-4 + ax + -1by))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = ((-60 + 15ax + -15by) + ax(-4 + ax + -1by) + -1by * (-4 + ax + -1by))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + (-4 * ax + ax * ax + -1by * ax) + -1by * (-4 + ax + -1by))

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + (-1abxy + -4ax + a2x2) + -1by * (-4 + ax + -1by))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + (-1abxy + -4ax + a2x2) + -1by * (-4 + ax + -1by))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + -1abxy + -4ax + a2x2 + (-4 * -1by + ax * -1by + -1by * -1by))

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + -1abxy + -4ax + a2x2 + (-1abxy + 4by + 1b2y2))
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + 15ax + -15by + -1abxy + -4ax + a2x2 + (-1abxy + 4by + 1b2y2))

Reorder the terms:
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + -1abxy + -1abxy + 15ax + -4ax + a2x2 + -15by + 4by + 1b2y2)

Combine like terms: -1abxy + -1abxy = -2abxy
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + -2abxy + 15ax + -4ax + a2x2 + -15by + 4by + 1b2y2)

Combine like terms: 15ax + -4ax = 11ax
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + -2abxy + 11ax + a2x2 + -15by + 4by + 1b2y2)

Combine like terms: -15by + 4by = -11by
-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = (-60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2)

Add '60' to each side of the equation.
-60 + -2abxy + 11ax + a2x2 + -11by + 60 + 1b2y2 = -60 + -2abxy + 11ax + a2x2 + -11by + 60 + 1b2y2

Reorder the terms:
-60 + 60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = -60 + -2abxy + 11ax + a2x2 + -11by + 60 + 1b2y2

Combine like terms: -60 + 60 = 0
0 + -2abxy + 11ax + a2x2 + -11by + 1b2y2 = -60 + -2abxy + 11ax + a2x2 + -11by + 60 + 1b2y2
-2abxy + 11ax + a2x2 + -11by + 1b2y2 = -60 + -2abxy + 11ax + a2x2 + -11by + 60 + 1b2y2

Reorder the terms:
-2abxy + 11ax + a2x2 + -11by + 1b2y2 = -60 + 60 + -2abxy + 11ax + a2x2 + -11by + 1b2y2

Combine like terms: -60 + 60 = 0
-2abxy + 11ax + a2x2 + -11by + 1b2y2 = 0 + -2abxy + 11ax + a2x2 + -11by + 1b2y2
-2abxy + 11ax + a2x2 + -11by + 1b2y2 = -2abxy + 11ax + a2x2 + -11by + 1b2y2

Add '2abxy' to each side of the equation.
-2abxy + 11ax + a2x2 + -11by + 2abxy + 1b2y2 = -2abxy + 11ax + a2x2 + -11by + 2abxy + 1b2y2

Reorder the terms:
-2abxy + 2abxy + 11ax + a2x2 + -11by + 1b2y2 = -2abxy + 11ax + a2x2 + -11by + 2abxy + 1b2y2

Combine like terms: -2abxy + 2abxy = 0
0 + 11ax + a2x2 + -11by + 1b2y2 = -2abxy + 11ax + a2x2 + -11by + 2abxy + 1b2y2
11ax + a2x2 + -11by + 1b2y2 = -2abxy + 11ax + a2x2 + -11by + 2abxy + 1b2y2

Reorder the terms:
11ax + a2x2 + -11by + 1b2y2 = -2abxy + 2abxy + 11ax + a2x2 + -11by + 1b2y2

Combine like terms: -2abxy + 2abxy = 0
11ax + a2x2 + -11by + 1b2y2 = 0 + 11ax + a2x2 + -11by + 1b2y2
11ax + a2x2 + -11by + 1b2y2 = 11ax + a2x2 + -11by + 1b2y2

Add '-11ax' to each side of the equation.
11ax + a2x2 + -11by + -11ax + 1b2y2 = 11ax + a2x2 + -11by + -11ax + 1b2y2

Reorder the terms:
11ax + -11ax + a2x2 + -11by + 1b2y2 = 11ax + a2x2 + -11by + -11ax + 1b2y2

Combine like terms: 11ax + -11ax = 0
0 + a2x2 + -11by + 1b2y2 = 11ax + a2x2 + -11by + -11ax + 1b2y2
a2x2 + -11by + 1b2y2 = 11ax + a2x2 + -11by + -11ax + 1b2y2

Reorder the terms:
a2x2 + -11by + 1b2y2 = 11ax + -11ax + a2x2 + -11by + 1b2y2

Combine like terms: 11ax + -11ax = 0
a2x2 + -11by + 1b2y2 = 0 + a2x2 + -11by + 1b2y2
a2x2 + -11by + 1b2y2 = a2x2 + -11by + 1b2y2

Add '-1a2x2' to each side of the equation.
a2x2 + -11by + -1a2x2 + 1b2y2 = a2x2 + -11by + -1a2x2 + 1b2y2

Reorder the terms:
a2x2 + -1a2x2 + -11by + 1b2y2 = a2x2 + -11by + -1a2x2 + 1b2y2

Combine like terms: a2x2 + -1a2x2 = 0
0 + -11by + 1b2y2 = a2x2 + -11by + -1a2x2 + 1b2y2
-11by + 1b2y2 = a2x2 + -11by + -1a2x2 + 1b2y2

Reorder the terms:
-11by + 1b2y2 = a2x2 + -1a2x2 + -11by + 1b2y2

Combine like terms: a2x2 + -1a2x2 = 0
-11by + 1b2y2 = 0 + -11by + 1b2y2
-11by + 1b2y2 = -11by + 1b2y2

Add '11by' to each side of the equation.
-11by + 11by + 1b2y2 = -11by + 11by + 1b2y2

Combine like terms: -11by + 11by = 0
0 + 1b2y2 = -11by + 11by + 1b2y2
1b2y2 = -11by + 11by + 1b2y2

Combine like terms: -11by + 11by = 0
1b2y2 = 0 + 1b2y2
1b2y2 = 1b2y2

Add '-1b2y2' to each side of the equation.
1b2y2 + -1b2y2 = 1b2y2 + -1b2y2

Combine like terms: 1b2y2 + -1b2y2 = 0
0 = 1b2y2 + -1b2y2

Combine like terms: 1b2y2 + -1b2y2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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