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

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


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

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

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

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

Combine like terms: -12x + 10x = -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 + x + -3x2) = 0

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

Ignore the factor 2.

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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