(3x-5)(x-6)=(2x+7)(x-6)

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Solution for (3x-5)(x-6)=(2x+7)(x-6) equation:


Simplifying
(3x + -5)(x + -6) = (2x + 7)(x + -6)

Reorder the terms:
(-5 + 3x)(x + -6) = (2x + 7)(x + -6)

Reorder the terms:
(-5 + 3x)(-6 + x) = (2x + 7)(x + -6)

Multiply (-5 + 3x) * (-6 + x)
(-5(-6 + x) + 3x * (-6 + x)) = (2x + 7)(x + -6)
((-6 * -5 + x * -5) + 3x * (-6 + x)) = (2x + 7)(x + -6)
((30 + -5x) + 3x * (-6 + x)) = (2x + 7)(x + -6)
(30 + -5x + (-6 * 3x + x * 3x)) = (2x + 7)(x + -6)
(30 + -5x + (-18x + 3x2)) = (2x + 7)(x + -6)

Combine like terms: -5x + -18x = -23x
(30 + -23x + 3x2) = (2x + 7)(x + -6)

Reorder the terms:
30 + -23x + 3x2 = (7 + 2x)(x + -6)

Reorder the terms:
30 + -23x + 3x2 = (7 + 2x)(-6 + x)

Multiply (7 + 2x) * (-6 + x)
30 + -23x + 3x2 = (7(-6 + x) + 2x * (-6 + x))
30 + -23x + 3x2 = ((-6 * 7 + x * 7) + 2x * (-6 + x))
30 + -23x + 3x2 = ((-42 + 7x) + 2x * (-6 + x))
30 + -23x + 3x2 = (-42 + 7x + (-6 * 2x + x * 2x))
30 + -23x + 3x2 = (-42 + 7x + (-12x + 2x2))

Combine like terms: 7x + -12x = -5x
30 + -23x + 3x2 = (-42 + -5x + 2x2)

Solving
30 + -23x + 3x2 = -42 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
30 + 42 + -23x + 5x + 3x2 + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Combine like terms: 30 + 42 = 72
72 + -23x + 5x + 3x2 + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Combine like terms: -23x + 5x = -18x
72 + -18x + 3x2 + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
72 + -18x + 1x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Reorder the terms:
72 + -18x + 1x2 = -42 + 42 + -5x + 5x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
72 + -18x + 1x2 = 0 + -5x + 5x + 2x2 + -2x2
72 + -18x + 1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
72 + -18x + 1x2 = 0 + 2x2 + -2x2
72 + -18x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
72 + -18x + 1x2 = 0

Factor a trinomial.
(6 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {6, 12}

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