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

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


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

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

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

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

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

Solving
0 = -10 + -1x + 3x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(2 + -1x)(5 + 3x) = 0


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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {2, -1.666666667}

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