(x-1)(x-5x+6)=

Solution for (x-1)(x-5x+6)= equation:

Simplifying
(x + -1)(x + -5x + 6) = 0

Reorder the terms:
(-1 + x)(x + -5x + 6) = 0

Reorder the terms:
(-1 + x)(6 + x + -5x) = 0

Combine like terms: x + -5x = -4x
(-1 + x)(6 + -4x) = 0

Multiply (-1 + x) * (6 + -4x)
(-1(6 + -4x) + x(6 + -4x)) = 0
((6 * -1 + -4x * -1) + x(6 + -4x)) = 0
((-6 + 4x) + x(6 + -4x)) = 0
(-6 + 4x + (6 * x + -4x * x)) = 0
(-6 + 4x + (6x + -4x2)) = 0

Combine like terms: 4x + 6x = 10x
(-6 + 10x + -4x2) = 0

Solving
-6 + 10x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5x + -2x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {1.5, 1}