(3x-4)(x-6)=(x-18)(2x+1)

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Solution for (3x-4)(x-6)=(x-18)(2x+1) equation: 


Simplifying
(3x + -4)(x + -6) = (x + -18)(2x + 1)

Reorder the terms:
(-4 + 3x)(x + -6) = (x + -18)(2x + 1)

Reorder the terms:
(-4 + 3x)(-6 + x) = (x + -18)(2x + 1)

Multiply (-4 + 3x) * (-6 + x)
(-4(-6 + x) + 3x * (-6 + x)) = (x + -18)(2x + 1)
((-6 * -4 + x * -4) + 3x * (-6 + x)) = (x + -18)(2x + 1)
((24 + -4x) + 3x * (-6 + x)) = (x + -18)(2x + 1)
(24 + -4x + (-6 * 3x + x * 3x)) = (x + -18)(2x + 1)
(24 + -4x + (-18x + 3x2)) = (x + -18)(2x + 1)

Combine like terms: -4x + -18x = -22x
(24 + -22x + 3x2) = (x + -18)(2x + 1)

Reorder the terms:
24 + -22x + 3x2 = (-18 + x)(2x + 1)

Reorder the terms:
24 + -22x + 3x2 = (-18 + x)(1 + 2x)

Multiply (-18 + x) * (1 + 2x)
24 + -22x + 3x2 = (-18(1 + 2x) + x(1 + 2x))
24 + -22x + 3x2 = ((1 * -18 + 2x * -18) + x(1 + 2x))
24 + -22x + 3x2 = ((-18 + -36x) + x(1 + 2x))
24 + -22x + 3x2 = (-18 + -36x + (1 * x + 2x * x))
24 + -22x + 3x2 = (-18 + -36x + (1x + 2x2))

Combine like terms: -36x + 1x = -35x
24 + -22x + 3x2 = (-18 + -35x + 2x2)

Solving
24 + -22x + 3x2 = -18 + -35x + 2x2

Solving for variable 'x'.

Reorder the terms:
24 + 18 + -22x + 35x + 3x2 + -2x2 = -18 + -35x + 2x2 + 18 + 35x + -2x2

Combine like terms: 24 + 18 = 42
42 + -22x + 35x + 3x2 + -2x2 = -18 + -35x + 2x2 + 18 + 35x + -2x2

Combine like terms: -22x + 35x = 13x
42 + 13x + 3x2 + -2x2 = -18 + -35x + 2x2 + 18 + 35x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
42 + 13x + 1x2 = -18 + -35x + 2x2 + 18 + 35x + -2x2

Reorder the terms:
42 + 13x + 1x2 = -18 + 18 + -35x + 35x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
42 + 13x + 1x2 = 0 + -35x + 35x + 2x2 + -2x2
42 + 13x + 1x2 = -35x + 35x + 2x2 + -2x2

Combine like terms: -35x + 35x = 0
42 + 13x + 1x2 = 0 + 2x2 + -2x2
42 + 13x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + 13x + 1x2 = 0

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-7, -6}

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