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

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


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

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

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

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

Combine like terms: -6x + 3x = -3x
(-9 + -3x + 2x2) + -5 = 0

Reorder the terms:
-9 + -5 + -3x + 2x2 = 0

Combine like terms: -9 + -5 = -14
-14 + -3x + 2x2 = 0

Solving
-14 + -3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(7 + -2x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-2, 3.5}

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