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

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


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

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

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

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

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

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

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

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

Combine like terms: -3x + -12x = -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.
(-4 + -1x)(8 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 8}

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