(x+3)(2x-1)=345

Solution for (x+3)(2x-1)=345 equation:

Simplifying
(x + 3)(2x + -1) = 345

Reorder the terms:
(3 + x)(2x + -1) = 345

Reorder the terms:
(3 + x)(-1 + 2x) = 345

Multiply (3 + x) * (-1 + 2x)
(3(-1 + 2x) + x(-1 + 2x)) = 345
((-1 * 3 + 2x * 3) + x(-1 + 2x)) = 345
((-3 + 6x) + x(-1 + 2x)) = 345
(-3 + 6x + (-1 * x + 2x * x)) = 345
(-3 + 6x + (-1x + 2x2)) = 345

Combine like terms: 6x + -1x = 5x
(-3 + 5x + 2x2) = 345

Solving
-3 + 5x + 2x2 = 345

Solving for variable 'x'.

Reorder the terms:
-3 + -345 + 5x + 2x2 = 345 + -345

Combine like terms: -3 + -345 = -348
-348 + 5x + 2x2 = 345 + -345

Combine like terms: 345 + -345 = 0
-348 + 5x + 2x2 = 0

Factor a trinomial.
(-29 + -2x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-29 + -2x)' equal to zero and attempt to solve:

Simplifying
-29 + -2x = 0

Solving
-29 + -2x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -2x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -2x = 0 + 29
-2x = 0 + 29

Combine like terms: 0 + 29 = 29
-2x = 29

Divide each side by '-2'.
x = -14.5

Simplifying
x = -14.5
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-14.5, 12}