4x(x-1)+(2x-6)=

Solution for 4x(x-1)+(2x-6)= equation:

Simplifying
4x(x + -1) + (2x + -6) = 0

Reorder the terms:
4x(-1 + x) + (2x + -6) = 0
(-1 * 4x + x * 4x) + (2x + -6) = 0
(-4x + 4x2) + (2x + -6) = 0

Reorder the terms:
-4x + 4x2 + (-6 + 2x) = 0

Remove parenthesis around (-6 + 2x)
-4x + 4x2 + -6 + 2x = 0

Reorder the terms:
-6 + -4x + 2x + 4x2 = 0

Combine like terms: -4x + 2x = -2x
-6 + -2x + 4x2 = 0

Solving
-6 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1x + 2x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -2x)) = 0

Ignore the factor 2.
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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}