(3x-2)(x+7)=(x+6)(2x+3)

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Solution for (3x-2)(x+7)=(x+6)(2x+3) equation: 


Simplifying
(3x + -2)(x + 7) = (x + 6)(2x + 3)

Reorder the terms:
(-2 + 3x)(x + 7) = (x + 6)(2x + 3)

Reorder the terms:
(-2 + 3x)(7 + x) = (x + 6)(2x + 3)

Multiply (-2 + 3x) * (7 + x)
(-2(7 + x) + 3x * (7 + x)) = (x + 6)(2x + 3)
((7 * -2 + x * -2) + 3x * (7 + x)) = (x + 6)(2x + 3)
((-14 + -2x) + 3x * (7 + x)) = (x + 6)(2x + 3)
(-14 + -2x + (7 * 3x + x * 3x)) = (x + 6)(2x + 3)
(-14 + -2x + (21x + 3x2)) = (x + 6)(2x + 3)

Combine like terms: -2x + 21x = 19x
(-14 + 19x + 3x2) = (x + 6)(2x + 3)

Reorder the terms:
-14 + 19x + 3x2 = (6 + x)(2x + 3)

Reorder the terms:
-14 + 19x + 3x2 = (6 + x)(3 + 2x)

Multiply (6 + x) * (3 + 2x)
-14 + 19x + 3x2 = (6(3 + 2x) + x(3 + 2x))
-14 + 19x + 3x2 = ((3 * 6 + 2x * 6) + x(3 + 2x))
-14 + 19x + 3x2 = ((18 + 12x) + x(3 + 2x))
-14 + 19x + 3x2 = (18 + 12x + (3 * x + 2x * x))
-14 + 19x + 3x2 = (18 + 12x + (3x + 2x2))

Combine like terms: 12x + 3x = 15x
-14 + 19x + 3x2 = (18 + 15x + 2x2)

Solving
-14 + 19x + 3x2 = 18 + 15x + 2x2

Solving for variable 'x'.

Reorder the terms:
-14 + -18 + 19x + -15x + 3x2 + -2x2 = 18 + 15x + 2x2 + -18 + -15x + -2x2

Combine like terms: -14 + -18 = -32
-32 + 19x + -15x + 3x2 + -2x2 = 18 + 15x + 2x2 + -18 + -15x + -2x2

Combine like terms: 19x + -15x = 4x
-32 + 4x + 3x2 + -2x2 = 18 + 15x + 2x2 + -18 + -15x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-32 + 4x + 1x2 = 18 + 15x + 2x2 + -18 + -15x + -2x2

Reorder the terms:
-32 + 4x + 1x2 = 18 + -18 + 15x + -15x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-32 + 4x + 1x2 = 0 + 15x + -15x + 2x2 + -2x2
-32 + 4x + 1x2 = 15x + -15x + 2x2 + -2x2

Combine like terms: 15x + -15x = 0
-32 + 4x + 1x2 = 0 + 2x2 + -2x2
-32 + 4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-32 + 4x + 1x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}

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