(2x-5)(x+3)=-14

Solution for (2x-5)(x+3)=-14 equation:

Simplifying
(2x + -5)(x + 3) = -14

Reorder the terms:
(-5 + 2x)(x + 3) = -14

Reorder the terms:
(-5 + 2x)(3 + x) = -14

Multiply (-5 + 2x) * (3 + x)
(-5(3 + x) + 2x * (3 + x)) = -14
((3 * -5 + x * -5) + 2x * (3 + x)) = -14
((-15 + -5x) + 2x * (3 + x)) = -14
(-15 + -5x + (3 * 2x + x * 2x)) = -14
(-15 + -5x + (6x + 2x2)) = -14

Combine like terms: -5x + 6x = 1x
(-15 + 1x + 2x2) = -14

Solving
-15 + 1x + 2x2 = -14

Solving for variable 'x'.

Reorder the terms:
-15 + 14 + 1x + 2x2 = -14 + 14

Combine like terms: -15 + 14 = -1
-1 + 1x + 2x2 = -14 + 14

Combine like terms: -14 + 14 = 0
-1 + 1x + 2x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1, 0.5}