(-x-2)*(3x-5)=(3x+1)*(x+3)

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Solution for (-x-2)*(3x-5)=(3x+1)*(x+3) equation: 


Simplifying
(-1x + -2)(3x + -5) = (3x + 1)(x + 3)

Reorder the terms:
(-2 + -1x)(3x + -5) = (3x + 1)(x + 3)

Reorder the terms:
(-2 + -1x)(-5 + 3x) = (3x + 1)(x + 3)

Multiply (-2 + -1x) * (-5 + 3x)
(-2(-5 + 3x) + -1x * (-5 + 3x)) = (3x + 1)(x + 3)
((-5 * -2 + 3x * -2) + -1x * (-5 + 3x)) = (3x + 1)(x + 3)
((10 + -6x) + -1x * (-5 + 3x)) = (3x + 1)(x + 3)
(10 + -6x + (-5 * -1x + 3x * -1x)) = (3x + 1)(x + 3)
(10 + -6x + (5x + -3x2)) = (3x + 1)(x + 3)

Combine like terms: -6x + 5x = -1x
(10 + -1x + -3x2) = (3x + 1)(x + 3)

Reorder the terms:
10 + -1x + -3x2 = (1 + 3x)(x + 3)

Reorder the terms:
10 + -1x + -3x2 = (1 + 3x)(3 + x)

Multiply (1 + 3x) * (3 + x)
10 + -1x + -3x2 = (1(3 + x) + 3x * (3 + x))
10 + -1x + -3x2 = ((3 * 1 + x * 1) + 3x * (3 + x))
10 + -1x + -3x2 = ((3 + 1x) + 3x * (3 + x))
10 + -1x + -3x2 = (3 + 1x + (3 * 3x + x * 3x))
10 + -1x + -3x2 = (3 + 1x + (9x + 3x2))

Combine like terms: 1x + 9x = 10x
10 + -1x + -3x2 = (3 + 10x + 3x2)

Solving
10 + -1x + -3x2 = 3 + 10x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + -3 + -1x + -10x + -3x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2

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

Combine like terms: -1x + -10x = -11x
7 + -11x + -3x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2

Combine like terms: -3x2 + -3x2 = -6x2
7 + -11x + -6x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2

Reorder the terms:
7 + -11x + -6x2 = 3 + -3 + 10x + -10x + 3x2 + -3x2

Combine like terms: 3 + -3 = 0
7 + -11x + -6x2 = 0 + 10x + -10x + 3x2 + -3x2
7 + -11x + -6x2 = 10x + -10x + 3x2 + -3x2

Combine like terms: 10x + -10x = 0
7 + -11x + -6x2 = 0 + 3x2 + -3x2
7 + -11x + -6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
7 + -11x + -6x2 = 0

Factor a trinomial.
(1 + -2x)(7 + 3x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0.5, -2.333333333}

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