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

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

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

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

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

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

Combine like terms: -5x + 6x = 1x
(-15 + 1x + 2x2) = 6

Solving
-15 + 1x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-15 + -6 + 1x + 2x2 = 6 + -6

Combine like terms: -15 + -6 = -21
-21 + 1x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-21 + 1x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(3 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.5, 3}