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

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

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

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

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

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

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

Solving
6 = -15 + -1x + 2x2

Solving for variable 'x'.

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

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

Combine like terms: -15 + 15 = 0
21 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2
21 + x + -2x2 = -1x + x + 2x2 + -2x2

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

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

Factor a trinomial.
(7 + -2x)(3 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

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