(3x+5)(x-2)+8=0

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Solution for (3x+5)(x-2)+8=0 equation: 


Simplifying
(3x + 5)(x + -2) + 8 = 0

Reorder the terms:
(5 + 3x)(x + -2) + 8 = 0

Reorder the terms:
(5 + 3x)(-2 + x) + 8 = 0

Multiply (5 + 3x) * (-2 + x)
(5(-2 + x) + 3x * (-2 + x)) + 8 = 0
((-2 * 5 + x * 5) + 3x * (-2 + x)) + 8 = 0
((-10 + 5x) + 3x * (-2 + x)) + 8 = 0
(-10 + 5x + (-2 * 3x + x * 3x)) + 8 = 0
(-10 + 5x + (-6x + 3x2)) + 8 = 0

Combine like terms: 5x + -6x = -1x
(-10 + -1x + 3x2) + 8 = 0

Reorder the terms:
-10 + 8 + -1x + 3x2 = 0

Combine like terms: -10 + 8 = -2
-2 + -1x + 3x2 = 0

Solving
-2 + -1x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.6666666667, 1}

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