(3x+6)*(4-5x)=0

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Solution for (3x+6)*(4-5x)=0 equation: 


Simplifying
(3x + 6)(4 + -5x) = 0

Reorder the terms:
(6 + 3x)(4 + -5x) = 0

Multiply (6 + 3x) * (4 + -5x)
(6(4 + -5x) + 3x * (4 + -5x)) = 0
((4 * 6 + -5x * 6) + 3x * (4 + -5x)) = 0
((24 + -30x) + 3x * (4 + -5x)) = 0
(24 + -30x + (4 * 3x + -5x * 3x)) = 0
(24 + -30x + (12x + -15x2)) = 0

Combine like terms: -30x + 12x = -18x
(24 + -18x + -15x2) = 0

Solving
24 + -18x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -6x + -5x2) = 0

Factor a trinomial.
3((4 + -5x)(2 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

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 = {0.8, -2}

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