0=(5x-2)(3x+6)

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Solution for 0=(5x-2)(3x+6) equation: 


Simplifying
0 = (5x + -2)(3x + 6)

Reorder the terms:
0 = (-2 + 5x)(3x + 6)

Reorder the terms:
0 = (-2 + 5x)(6 + 3x)

Multiply (-2 + 5x) * (6 + 3x)
0 = (-2(6 + 3x) + 5x * (6 + 3x))
0 = ((6 * -2 + 3x * -2) + 5x * (6 + 3x))
0 = ((-12 + -6x) + 5x * (6 + 3x))
0 = (-12 + -6x + (6 * 5x + 3x * 5x))
0 = (-12 + -6x + (30x + 15x2))

Combine like terms: -6x + 30x = 24x
0 = (-12 + 24x + 15x2)

Solving
0 = -12 + 24x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + -24x + -15x2 = -12 + 24x + 15x2 + 12 + -24x + -15x2

Reorder the terms:
12 + -24x + -15x2 = -12 + 12 + 24x + -24x + 15x2 + -15x2

Combine like terms: -12 + 12 = 0
12 + -24x + -15x2 = 0 + 24x + -24x + 15x2 + -15x2
12 + -24x + -15x2 = 24x + -24x + 15x2 + -15x2

Combine like terms: 24x + -24x = 0
12 + -24x + -15x2 = 0 + 15x2 + -15x2
12 + -24x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
12 + -24x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -8x + -5x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

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 = {0.4, -2}

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