(6x-16)(x-6)=(5x-18)(x-7)

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Solution for (6x-16)(x-6)=(5x-18)(x-7) equation: 


Simplifying
(6x + -16)(x + -6) = (5x + -18)(x + -7)

Reorder the terms:
(-16 + 6x)(x + -6) = (5x + -18)(x + -7)

Reorder the terms:
(-16 + 6x)(-6 + x) = (5x + -18)(x + -7)

Multiply (-16 + 6x) * (-6 + x)
(-16(-6 + x) + 6x * (-6 + x)) = (5x + -18)(x + -7)
((-6 * -16 + x * -16) + 6x * (-6 + x)) = (5x + -18)(x + -7)
((96 + -16x) + 6x * (-6 + x)) = (5x + -18)(x + -7)
(96 + -16x + (-6 * 6x + x * 6x)) = (5x + -18)(x + -7)
(96 + -16x + (-36x + 6x2)) = (5x + -18)(x + -7)

Combine like terms: -16x + -36x = -52x
(96 + -52x + 6x2) = (5x + -18)(x + -7)

Reorder the terms:
96 + -52x + 6x2 = (-18 + 5x)(x + -7)

Reorder the terms:
96 + -52x + 6x2 = (-18 + 5x)(-7 + x)

Multiply (-18 + 5x) * (-7 + x)
96 + -52x + 6x2 = (-18(-7 + x) + 5x * (-7 + x))
96 + -52x + 6x2 = ((-7 * -18 + x * -18) + 5x * (-7 + x))
96 + -52x + 6x2 = ((126 + -18x) + 5x * (-7 + x))
96 + -52x + 6x2 = (126 + -18x + (-7 * 5x + x * 5x))
96 + -52x + 6x2 = (126 + -18x + (-35x + 5x2))

Combine like terms: -18x + -35x = -53x
96 + -52x + 6x2 = (126 + -53x + 5x2)

Solving
96 + -52x + 6x2 = 126 + -53x + 5x2

Solving for variable 'x'.

Reorder the terms:
96 + -126 + -52x + 53x + 6x2 + -5x2 = 126 + -53x + 5x2 + -126 + 53x + -5x2

Combine like terms: 96 + -126 = -30
-30 + -52x + 53x + 6x2 + -5x2 = 126 + -53x + 5x2 + -126 + 53x + -5x2

Combine like terms: -52x + 53x = 1x
-30 + 1x + 6x2 + -5x2 = 126 + -53x + 5x2 + -126 + 53x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
-30 + 1x + 1x2 = 126 + -53x + 5x2 + -126 + 53x + -5x2

Reorder the terms:
-30 + 1x + 1x2 = 126 + -126 + -53x + 53x + 5x2 + -5x2

Combine like terms: 126 + -126 = 0
-30 + 1x + 1x2 = 0 + -53x + 53x + 5x2 + -5x2
-30 + 1x + 1x2 = -53x + 53x + 5x2 + -5x2

Combine like terms: -53x + 53x = 0
-30 + 1x + 1x2 = 0 + 5x2 + -5x2
-30 + 1x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-30 + 1x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}

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