(2x+3)(x-5)=6x+9

Solution for (2x+3)(x-5)=6x+9 equation:

Simplifying
(2x + 3)(x + -5) = 6x + 9

Reorder the terms:
(3 + 2x)(x + -5) = 6x + 9

Reorder the terms:
(3 + 2x)(-5 + x) = 6x + 9

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) = 6x + 9
((-5 * 3 + x * 3) + 2x * (-5 + x)) = 6x + 9
((-15 + 3x) + 2x * (-5 + x)) = 6x + 9
(-15 + 3x + (-5 * 2x + x * 2x)) = 6x + 9
(-15 + 3x + (-10x + 2x2)) = 6x + 9

Combine like terms: 3x + -10x = -7x
(-15 + -7x + 2x2) = 6x + 9

Reorder the terms:
-15 + -7x + 2x2 = 9 + 6x

Solving
-15 + -7x + 2x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
-15 + -9 + -7x + -6x + 2x2 = 9 + 6x + -9 + -6x

Combine like terms: -15 + -9 = -24
-24 + -7x + -6x + 2x2 = 9 + 6x + -9 + -6x

Combine like terms: -7x + -6x = -13x
-24 + -13x + 2x2 = 9 + 6x + -9 + -6x

Reorder the terms:
-24 + -13x + 2x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
-24 + -13x + 2x2 = 0 + 6x + -6x
-24 + -13x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-24 + -13x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1.5, 8}