(x-2)(x+3)=50

Solution for (x-2)(x+3)=50 equation:

Simplifying
(x + -2)(x + 3) = 50

Reorder the terms:
(-2 + x)(x + 3) = 50

Reorder the terms:
(-2 + x)(3 + x) = 50

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = 50
((3 * -2 + x * -2) + x(3 + x)) = 50
((-6 + -2x) + x(3 + x)) = 50
(-6 + -2x + (3 * x + x * x)) = 50
(-6 + -2x + (3x + x2)) = 50

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = 50

Solving
-6 + 1x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
-6 + -50 + 1x + x2 = 50 + -50

Combine like terms: -6 + -50 = -56
-56 + 1x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-56 + 1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-8, 7}