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

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

Simplifying
(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 + -2x)(1 + x) = 0

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

Simplifying
1 + x = 0

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

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

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

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