(x-1)(2x+3)=(x-1)(x-6)

Solution for (x-1)(2x+3)=(x-1)(x-6) equation:

Simplifying
(x + -1)(2x + 3) = (x + -1)(x + -6)

Reorder the terms:
(-1 + x)(2x + 3) = (x + -1)(x + -6)

Reorder the terms:
(-1 + x)(3 + 2x) = (x + -1)(x + -6)

Multiply (-1 + x) * (3 + 2x)
(-1(3 + 2x) + x(3 + 2x)) = (x + -1)(x + -6)
((3 * -1 + 2x * -1) + x(3 + 2x)) = (x + -1)(x + -6)
((-3 + -2x) + x(3 + 2x)) = (x + -1)(x + -6)
(-3 + -2x + (3 * x + 2x * x)) = (x + -1)(x + -6)
(-3 + -2x + (3x + 2x2)) = (x + -1)(x + -6)

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

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

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

Multiply (-1 + x) * (-6 + x)
-3 + 1x + 2x2 = (-1(-6 + x) + x(-6 + x))
-3 + 1x + 2x2 = ((-6 * -1 + x * -1) + x(-6 + x))
-3 + 1x + 2x2 = ((6 + -1x) + x(-6 + x))
-3 + 1x + 2x2 = (6 + -1x + (-6 * x + x * x))
-3 + 1x + 2x2 = (6 + -1x + (-6x + x2))

Combine like terms: -1x + -6x = -7x
-3 + 1x + 2x2 = (6 + -7x + x2)

Solving
-3 + 1x + 2x2 = 6 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -6 + 1x + 7x + 2x2 + -1x2 = 6 + -7x + x2 + -6 + 7x + -1x2

Combine like terms: -3 + -6 = -9
-9 + 1x + 7x + 2x2 + -1x2 = 6 + -7x + x2 + -6 + 7x + -1x2

Combine like terms: 1x + 7x = 8x
-9 + 8x + 2x2 + -1x2 = 6 + -7x + x2 + -6 + 7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-9 + 8x + 1x2 = 6 + -7x + x2 + -6 + 7x + -1x2

Reorder the terms:
-9 + 8x + 1x2 = 6 + -6 + -7x + 7x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-9 + 8x + 1x2 = 0 + -7x + 7x + x2 + -1x2
-9 + 8x + 1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-9 + 8x + 1x2 = 0 + x2 + -1x2
-9 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 8x + 1x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 1}