(3x+2)(x-5)=(x-14)(2x+3)

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Solution for (3x+2)(x-5)=(x-14)(2x+3) equation: 


Simplifying
(3x + 2)(x + -5) = (x + -14)(2x + 3)

Reorder the terms:
(2 + 3x)(x + -5) = (x + -14)(2x + 3)

Reorder the terms:
(2 + 3x)(-5 + x) = (x + -14)(2x + 3)

Multiply (2 + 3x) * (-5 + x)
(2(-5 + x) + 3x * (-5 + x)) = (x + -14)(2x + 3)
((-5 * 2 + x * 2) + 3x * (-5 + x)) = (x + -14)(2x + 3)
((-10 + 2x) + 3x * (-5 + x)) = (x + -14)(2x + 3)
(-10 + 2x + (-5 * 3x + x * 3x)) = (x + -14)(2x + 3)
(-10 + 2x + (-15x + 3x2)) = (x + -14)(2x + 3)

Combine like terms: 2x + -15x = -13x
(-10 + -13x + 3x2) = (x + -14)(2x + 3)

Reorder the terms:
-10 + -13x + 3x2 = (-14 + x)(2x + 3)

Reorder the terms:
-10 + -13x + 3x2 = (-14 + x)(3 + 2x)

Multiply (-14 + x) * (3 + 2x)
-10 + -13x + 3x2 = (-14(3 + 2x) + x(3 + 2x))
-10 + -13x + 3x2 = ((3 * -14 + 2x * -14) + x(3 + 2x))
-10 + -13x + 3x2 = ((-42 + -28x) + x(3 + 2x))
-10 + -13x + 3x2 = (-42 + -28x + (3 * x + 2x * x))
-10 + -13x + 3x2 = (-42 + -28x + (3x + 2x2))

Combine like terms: -28x + 3x = -25x
-10 + -13x + 3x2 = (-42 + -25x + 2x2)

Solving
-10 + -13x + 3x2 = -42 + -25x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 42 + -13x + 25x + 3x2 + -2x2 = -42 + -25x + 2x2 + 42 + 25x + -2x2

Combine like terms: -10 + 42 = 32
32 + -13x + 25x + 3x2 + -2x2 = -42 + -25x + 2x2 + 42 + 25x + -2x2

Combine like terms: -13x + 25x = 12x
32 + 12x + 3x2 + -2x2 = -42 + -25x + 2x2 + 42 + 25x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
32 + 12x + 1x2 = -42 + -25x + 2x2 + 42 + 25x + -2x2

Reorder the terms:
32 + 12x + 1x2 = -42 + 42 + -25x + 25x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
32 + 12x + 1x2 = 0 + -25x + 25x + 2x2 + -2x2
32 + 12x + 1x2 = -25x + 25x + 2x2 + -2x2

Combine like terms: -25x + 25x = 0
32 + 12x + 1x2 = 0 + 2x2 + -2x2
32 + 12x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + 12x + 1x2 = 0

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


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

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

Simplifying
x = -8

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

Simplifying
4 + x = 0

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

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

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

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

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