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

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


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

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

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

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

Combine like terms: -6x + -15x = -21x
2(-15 + -21x + -6x2) = 0
(-15 * 2 + -21x * 2 + -6x2 * 2) = 0
(-30 + -42x + -12x2) = 0

Solving
-30 + -42x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(5 + 7x + 2x2) = 0

Factor a trinomial.
-6((5 + 2x)(1 + x)) = 0

Ignore the factor -6.

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

Simplifying
5 + 2x = 0

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

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2.5, -1}

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