(x+3)(2x-1)=15

Solution for (x+3)(2x-1)=15 equation:

Simplifying
(x + 3)(2x + -1) = 15

Reorder the terms:
(3 + x)(2x + -1) = 15

Reorder the terms:
(3 + x)(-1 + 2x) = 15

Multiply (3 + x) * (-1 + 2x)
(3(-1 + 2x) + x(-1 + 2x)) = 15
((-1 * 3 + 2x * 3) + x(-1 + 2x)) = 15
((-3 + 6x) + x(-1 + 2x)) = 15
(-3 + 6x + (-1 * x + 2x * x)) = 15
(-3 + 6x + (-1x + 2x2)) = 15

Combine like terms: 6x + -1x = 5x
(-3 + 5x + 2x2) = 15

Solving
-3 + 5x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-3 + -15 + 5x + 2x2 = 15 + -15

Combine like terms: -3 + -15 = -18
-18 + 5x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-18 + 5x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.5, 2}