(x-6)(3x-4)=(x-14)(2x-1)

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Solution for (x-6)(3x-4)=(x-14)(2x-1) equation: 


Simplifying
(x + -6)(3x + -4) = (x + -14)(2x + -1)

Reorder the terms:
(-6 + x)(3x + -4) = (x + -14)(2x + -1)

Reorder the terms:
(-6 + x)(-4 + 3x) = (x + -14)(2x + -1)

Multiply (-6 + x) * (-4 + 3x)
(-6(-4 + 3x) + x(-4 + 3x)) = (x + -14)(2x + -1)
((-4 * -6 + 3x * -6) + x(-4 + 3x)) = (x + -14)(2x + -1)
((24 + -18x) + x(-4 + 3x)) = (x + -14)(2x + -1)
(24 + -18x + (-4 * x + 3x * x)) = (x + -14)(2x + -1)
(24 + -18x + (-4x + 3x2)) = (x + -14)(2x + -1)

Combine like terms: -18x + -4x = -22x
(24 + -22x + 3x2) = (x + -14)(2x + -1)

Reorder the terms:
24 + -22x + 3x2 = (-14 + x)(2x + -1)

Reorder the terms:
24 + -22x + 3x2 = (-14 + x)(-1 + 2x)

Multiply (-14 + x) * (-1 + 2x)
24 + -22x + 3x2 = (-14(-1 + 2x) + x(-1 + 2x))
24 + -22x + 3x2 = ((-1 * -14 + 2x * -14) + x(-1 + 2x))
24 + -22x + 3x2 = ((14 + -28x) + x(-1 + 2x))
24 + -22x + 3x2 = (14 + -28x + (-1 * x + 2x * x))
24 + -22x + 3x2 = (14 + -28x + (-1x + 2x2))

Combine like terms: -28x + -1x = -29x
24 + -22x + 3x2 = (14 + -29x + 2x2)

Solving
24 + -22x + 3x2 = 14 + -29x + 2x2

Solving for variable 'x'.

Reorder the terms:
24 + -14 + -22x + 29x + 3x2 + -2x2 = 14 + -29x + 2x2 + -14 + 29x + -2x2

Combine like terms: 24 + -14 = 10
10 + -22x + 29x + 3x2 + -2x2 = 14 + -29x + 2x2 + -14 + 29x + -2x2

Combine like terms: -22x + 29x = 7x
10 + 7x + 3x2 + -2x2 = 14 + -29x + 2x2 + -14 + 29x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
10 + 7x + 1x2 = 14 + -29x + 2x2 + -14 + 29x + -2x2

Reorder the terms:
10 + 7x + 1x2 = 14 + -14 + -29x + 29x + 2x2 + -2x2

Combine like terms: 14 + -14 = 0
10 + 7x + 1x2 = 0 + -29x + 29x + 2x2 + -2x2
10 + 7x + 1x2 = -29x + 29x + 2x2 + -2x2

Combine like terms: -29x + 29x = 0
10 + 7x + 1x2 = 0 + 2x2 + -2x2
10 + 7x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + 7x + 1x2 = 0

Factor a trinomial.
(5 + x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-5, -2}

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