(x-6)(3x-2)=(x-16)(2x+1)

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Solution for (x-6)(3x-2)=(x-16)(2x+1) equation: 


Simplifying
(x + -6)(3x + -2) = (x + -16)(2x + 1)

Reorder the terms:
(-6 + x)(3x + -2) = (x + -16)(2x + 1)

Reorder the terms:
(-6 + x)(-2 + 3x) = (x + -16)(2x + 1)

Multiply (-6 + x) * (-2 + 3x)
(-6(-2 + 3x) + x(-2 + 3x)) = (x + -16)(2x + 1)
((-2 * -6 + 3x * -6) + x(-2 + 3x)) = (x + -16)(2x + 1)
((12 + -18x) + x(-2 + 3x)) = (x + -16)(2x + 1)
(12 + -18x + (-2 * x + 3x * x)) = (x + -16)(2x + 1)
(12 + -18x + (-2x + 3x2)) = (x + -16)(2x + 1)

Combine like terms: -18x + -2x = -20x
(12 + -20x + 3x2) = (x + -16)(2x + 1)

Reorder the terms:
12 + -20x + 3x2 = (-16 + x)(2x + 1)

Reorder the terms:
12 + -20x + 3x2 = (-16 + x)(1 + 2x)

Multiply (-16 + x) * (1 + 2x)
12 + -20x + 3x2 = (-16(1 + 2x) + x(1 + 2x))
12 + -20x + 3x2 = ((1 * -16 + 2x * -16) + x(1 + 2x))
12 + -20x + 3x2 = ((-16 + -32x) + x(1 + 2x))
12 + -20x + 3x2 = (-16 + -32x + (1 * x + 2x * x))
12 + -20x + 3x2 = (-16 + -32x + (1x + 2x2))

Combine like terms: -32x + 1x = -31x
12 + -20x + 3x2 = (-16 + -31x + 2x2)

Solving
12 + -20x + 3x2 = -16 + -31x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + 16 + -20x + 31x + 3x2 + -2x2 = -16 + -31x + 2x2 + 16 + 31x + -2x2

Combine like terms: 12 + 16 = 28
28 + -20x + 31x + 3x2 + -2x2 = -16 + -31x + 2x2 + 16 + 31x + -2x2

Combine like terms: -20x + 31x = 11x
28 + 11x + 3x2 + -2x2 = -16 + -31x + 2x2 + 16 + 31x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
28 + 11x + 1x2 = -16 + -31x + 2x2 + 16 + 31x + -2x2

Reorder the terms:
28 + 11x + 1x2 = -16 + 16 + -31x + 31x + 2x2 + -2x2

Combine like terms: -16 + 16 = 0
28 + 11x + 1x2 = 0 + -31x + 31x + 2x2 + -2x2
28 + 11x + 1x2 = -31x + 31x + 2x2 + -2x2

Combine like terms: -31x + 31x = 0
28 + 11x + 1x2 = 0 + 2x2 + -2x2
28 + 11x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
28 + 11x + 1x2 = 0

Factor a trinomial.
(7 + x)(4 + x) = 0


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-7, -4}

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