(2x+3)(x-3)=11

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Solution for (2x+3)(x-3)=11 equation: 


Simplifying
(2x + 3)(x + -3) = 11

Reorder the terms:
(3 + 2x)(x + -3) = 11

Reorder the terms:
(3 + 2x)(-3 + x) = 11

Multiply (3 + 2x) * (-3 + x)
(3(-3 + x) + 2x * (-3 + x)) = 11
((-3 * 3 + x * 3) + 2x * (-3 + x)) = 11
((-9 + 3x) + 2x * (-3 + x)) = 11
(-9 + 3x + (-3 * 2x + x * 2x)) = 11
(-9 + 3x + (-6x + 2x2)) = 11

Combine like terms: 3x + -6x = -3x
(-9 + -3x + 2x2) = 11

Solving
-9 + -3x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
-9 + -11 + -3x + 2x2 = 11 + -11

Combine like terms: -9 + -11 = -20
-20 + -3x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-20 + -3x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2.5, 4}

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