(2x-6)(x+1)=10

Solution for (2x-6)(x+1)=10 equation:

Simplifying
(2x + -6)(x + 1) = 10

Reorder the terms:
(-6 + 2x)(x + 1) = 10

Reorder the terms:
(-6 + 2x)(1 + x) = 10

Multiply (-6 + 2x) * (1 + x)
(-6(1 + x) + 2x * (1 + x)) = 10
((1 * -6 + x * -6) + 2x * (1 + x)) = 10
((-6 + -6x) + 2x * (1 + x)) = 10
(-6 + -6x + (1 * 2x + x * 2x)) = 10
(-6 + -6x + (2x + 2x2)) = 10

Combine like terms: -6x + 2x = -4x
(-6 + -4x + 2x2) = 10

Solving
-6 + -4x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + -4x + 2x2 = 10 + -10

Combine like terms: -6 + -10 = -16
-16 + -4x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-16 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(4 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}