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

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

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

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

Combine like terms: 3x + -2x = 1x
(-3 + 1x)(x + 4x + 5) = 0

Reorder the terms:
(-3 + 1x)(5 + x + 4x) = 0

Combine like terms: x + 4x = 5x
(-3 + 1x)(5 + 5x) = 0

Multiply (-3 + 1x) * (5 + 5x)
(-3(5 + 5x) + 1x * (5 + 5x)) = 0
((5 * -3 + 5x * -3) + 1x * (5 + 5x)) = 0
((-15 + -15x) + 1x * (5 + 5x)) = 0
(-15 + -15x + (5 * 1x + 5x * 1x)) = 0
(-15 + -15x + (5x + 5x2)) = 0

Combine like terms: -15x + 5x = -10x
(-15 + -10x + 5x2) = 0

Solving
-15 + -10x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}