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

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


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

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

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

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

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

Solving
-9 + -3x + 2x2 = 5

Solving for variable 'x'.

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

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

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

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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