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

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


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

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

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

Multiply (-3 + 2x) * (5 + 3x)
(-3(5 + 3x) + 2x * (5 + 3x)) = 0
((5 * -3 + 3x * -3) + 2x * (5 + 3x)) = 0
((-15 + -9x) + 2x * (5 + 3x)) = 0
(-15 + -9x + (5 * 2x + 3x * 2x)) = 0
(-15 + -9x + (10x + 6x2)) = 0

Combine like terms: -9x + 10x = 1x
(-15 + 1x + 6x2) = 0

Solving
-15 + 1x + 6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.666666667, 1.5}

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