0=(3x-5)(2x+4)

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Solution for 0=(3x-5)(2x+4) equation: 


Simplifying
0 = (3x + -5)(2x + 4)

Reorder the terms:
0 = (-5 + 3x)(2x + 4)

Reorder the terms:
0 = (-5 + 3x)(4 + 2x)

Multiply (-5 + 3x) * (4 + 2x)
0 = (-5(4 + 2x) + 3x * (4 + 2x))
0 = ((4 * -5 + 2x * -5) + 3x * (4 + 2x))
0 = ((-20 + -10x) + 3x * (4 + 2x))
0 = (-20 + -10x + (4 * 3x + 2x * 3x))
0 = (-20 + -10x + (12x + 6x2))

Combine like terms: -10x + 12x = 2x
0 = (-20 + 2x + 6x2)

Solving
0 = -20 + 2x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -2x + -6x2 = -20 + 2x + 6x2 + 20 + -2x + -6x2

Reorder the terms:
20 + -2x + -6x2 = -20 + 20 + 2x + -2x + 6x2 + -6x2

Combine like terms: -20 + 20 = 0
20 + -2x + -6x2 = 0 + 2x + -2x + 6x2 + -6x2
20 + -2x + -6x2 = 2x + -2x + 6x2 + -6x2

Combine like terms: 2x + -2x = 0
20 + -2x + -6x2 = 0 + 6x2 + -6x2
20 + -2x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
20 + -2x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -1x + -3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
2 + x = 0

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

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

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

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

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