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

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


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

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

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

Multiply (-4 + 3x) * (2 + x)
(-4(2 + x) + 3x * (2 + x)) = (x + 6)(2x + -3)
((2 * -4 + x * -4) + 3x * (2 + x)) = (x + 6)(2x + -3)
((-8 + -4x) + 3x * (2 + x)) = (x + 6)(2x + -3)
(-8 + -4x + (2 * 3x + x * 3x)) = (x + 6)(2x + -3)
(-8 + -4x + (6x + 3x2)) = (x + 6)(2x + -3)

Combine like terms: -4x + 6x = 2x
(-8 + 2x + 3x2) = (x + 6)(2x + -3)

Reorder the terms:
-8 + 2x + 3x2 = (6 + x)(2x + -3)

Reorder the terms:
-8 + 2x + 3x2 = (6 + x)(-3 + 2x)

Multiply (6 + x) * (-3 + 2x)
-8 + 2x + 3x2 = (6(-3 + 2x) + x(-3 + 2x))
-8 + 2x + 3x2 = ((-3 * 6 + 2x * 6) + x(-3 + 2x))
-8 + 2x + 3x2 = ((-18 + 12x) + x(-3 + 2x))
-8 + 2x + 3x2 = (-18 + 12x + (-3 * x + 2x * x))
-8 + 2x + 3x2 = (-18 + 12x + (-3x + 2x2))

Combine like terms: 12x + -3x = 9x
-8 + 2x + 3x2 = (-18 + 9x + 2x2)

Solving
-8 + 2x + 3x2 = -18 + 9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 18 + 2x + -9x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2

Combine like terms: -8 + 18 = 10
10 + 2x + -9x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2

Combine like terms: 2x + -9x = -7x
10 + -7x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
10 + -7x + 1x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2

Reorder the terms:
10 + -7x + 1x2 = -18 + 18 + 9x + -9x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
10 + -7x + 1x2 = 0 + 9x + -9x + 2x2 + -2x2
10 + -7x + 1x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 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.
(2 + -1x)(5 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 5}

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