(3x-5)(x+2)=-8

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Solution for (3x-5)(x+2)=-8 equation: 


Simplifying
(3x + -5)(x + 2) = -8

Reorder the terms:
(-5 + 3x)(x + 2) = -8

Reorder the terms:
(-5 + 3x)(2 + x) = -8

Multiply (-5 + 3x) * (2 + x)
(-5(2 + x) + 3x * (2 + x)) = -8
((2 * -5 + x * -5) + 3x * (2 + x)) = -8
((-10 + -5x) + 3x * (2 + x)) = -8
(-10 + -5x + (2 * 3x + x * 3x)) = -8
(-10 + -5x + (6x + 3x2)) = -8

Combine like terms: -5x + 6x = 1x
(-10 + 1x + 3x2) = -8

Solving
-10 + 1x + 3x2 = -8

Solving for variable 'x'.

Reorder the terms:
-10 + 8 + 1x + 3x2 = -8 + 8

Combine like terms: -10 + 8 = -2
-2 + 1x + 3x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-2 + 1x + 3x2 = 0

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


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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1, 0.6666666667}

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