45(x-1)60(x-2)=60(x-2)

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Solution for 45(x-1)60(x-2)=60(x-2) equation: 


Simplifying
45(x + -1) * 60(x + -2) = 60(x + -2)

Reorder the terms:
45(-1 + x) * 60(x + -2) = 60(x + -2)

Reorder the terms:
45(-1 + x) * 60(-2 + x) = 60(x + -2)

Reorder the terms for easier multiplication:
45 * 60(-1 + x)(-2 + x) = 60(x + -2)

Multiply 45 * 60
2700(-1 + x)(-2 + x) = 60(x + -2)

Multiply (-1 + x) * (-2 + x)
2700(-1(-2 + x) + x(-2 + x)) = 60(x + -2)
2700((-2 * -1 + x * -1) + x(-2 + x)) = 60(x + -2)
2700((2 + -1x) + x(-2 + x)) = 60(x + -2)
2700(2 + -1x + (-2 * x + x * x)) = 60(x + -2)
2700(2 + -1x + (-2x + x2)) = 60(x + -2)

Combine like terms: -1x + -2x = -3x
2700(2 + -3x + x2) = 60(x + -2)
(2 * 2700 + -3x * 2700 + x2 * 2700) = 60(x + -2)
(5400 + -8100x + 2700x2) = 60(x + -2)

Reorder the terms:
5400 + -8100x + 2700x2 = 60(-2 + x)
5400 + -8100x + 2700x2 = (-2 * 60 + x * 60)
5400 + -8100x + 2700x2 = (-120 + 60x)

Solving
5400 + -8100x + 2700x2 = -120 + 60x

Solving for variable 'x'.

Reorder the terms:
5400 + 120 + -8100x + -60x + 2700x2 = -120 + 60x + 120 + -60x

Combine like terms: 5400 + 120 = 5520
5520 + -8100x + -60x + 2700x2 = -120 + 60x + 120 + -60x

Combine like terms: -8100x + -60x = -8160x
5520 + -8160x + 2700x2 = -120 + 60x + 120 + -60x

Reorder the terms:
5520 + -8160x + 2700x2 = -120 + 120 + 60x + -60x

Combine like terms: -120 + 120 = 0
5520 + -8160x + 2700x2 = 0 + 60x + -60x
5520 + -8160x + 2700x2 = 60x + -60x

Combine like terms: 60x + -60x = 0
5520 + -8160x + 2700x2 = 0

Factor out the Greatest Common Factor (GCF), '60'.
60(92 + -136x + 45x2) = 0

Factor a trinomial.
60((46 + -45x)(2 + -1x)) = 0

Ignore the factor 60.

Subproblem 1
Set the factor '(46 + -45x)' equal to zero and attempt to solve:

Simplifying
46 + -45x = 0

Solving
46 + -45x = 0

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

Add '-46' to each side of the equation.
46 + -46 + -45x = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -45x = 0 + -46
-45x = 0 + -46

Combine like terms: 0 + -46 = -46
-45x = -46

Divide each side by '-45'.
x = 1.022222222

Simplifying
x = 1.022222222

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.022222222, 2}

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