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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.5, 1.666666667}

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