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

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


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

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

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

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

Combine like terms: -15x + 6x = -9x
(-15 + -9x + 6x2) = 0

Solving
-15 + -9x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

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 '(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
Solution
x = {-1, 2.5}

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