2(x+3)(x-1)-x(x+3)=50

Solution for 2(x+3)(x-1)-x(x+3)=50 equation:

Simplifying
2(x + 3)(x + -1) + -1x(x + 3) = 50

Reorder the terms:
2(3 + x)(x + -1) + -1x(x + 3) = 50

Reorder the terms:
2(3 + x)(-1 + x) + -1x(x + 3) = 50

Multiply (3 + x) * (-1 + x)
2(3(-1 + x) + x(-1 + x)) + -1x(x + 3) = 50
2((-1 * 3 + x * 3) + x(-1 + x)) + -1x(x + 3) = 50
2((-3 + 3x) + x(-1 + x)) + -1x(x + 3) = 50
2(-3 + 3x + (-1 * x + x * x)) + -1x(x + 3) = 50
2(-3 + 3x + (-1x + x2)) + -1x(x + 3) = 50

Combine like terms: 3x + -1x = 2x
2(-3 + 2x + x2) + -1x(x + 3) = 50
(-3 * 2 + 2x * 2 + x2 * 2) + -1x(x + 3) = 50
(-6 + 4x + 2x2) + -1x(x + 3) = 50

Reorder the terms:
-6 + 4x + 2x2 + -1x(3 + x) = 50
-6 + 4x + 2x2 + (3 * -1x + x * -1x) = 50
-6 + 4x + 2x2 + (-3x + -1x2) = 50

Reorder the terms:
-6 + 4x + -3x + 2x2 + -1x2 = 50

Combine like terms: 4x + -3x = 1x
-6 + 1x + 2x2 + -1x2 = 50

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

Solving
-6 + 1x + 1x2 = 50

Solving for variable 'x'.

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

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

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