(x-3)*(2x+3)=45

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Solution for (x-3)*(2x+3)=45 equation: 


Simplifying
(x + -3)(2x + 3) = 45

Reorder the terms:
(-3 + x)(2x + 3) = 45

Reorder the terms:
(-3 + x)(3 + 2x) = 45

Multiply (-3 + x) * (3 + 2x)
(-3(3 + 2x) + x(3 + 2x)) = 45
((3 * -3 + 2x * -3) + x(3 + 2x)) = 45
((-9 + -6x) + x(3 + 2x)) = 45
(-9 + -6x + (3 * x + 2x * x)) = 45
(-9 + -6x + (3x + 2x2)) = 45

Combine like terms: -6x + 3x = -3x
(-9 + -3x + 2x2) = 45

Solving
-9 + -3x + 2x2 = 45

Solving for variable 'x'.

Reorder the terms:
-9 + -45 + -3x + 2x2 = 45 + -45

Combine like terms: -9 + -45 = -54
-54 + -3x + 2x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-54 + -3x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4.5, 6}

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