(x-2)(2x-3)=(x-2)(x+5)

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Solution for (x-2)(2x-3)=(x-2)(x+5) equation:


Simplifying
(x + -2)(2x + -3) = (x + -2)(x + 5)

Reorder the terms:
(-2 + x)(2x + -3) = (x + -2)(x + 5)

Reorder the terms:
(-2 + x)(-3 + 2x) = (x + -2)(x + 5)

Multiply (-2 + x) * (-3 + 2x)
(-2(-3 + 2x) + x(-3 + 2x)) = (x + -2)(x + 5)
((-3 * -2 + 2x * -2) + x(-3 + 2x)) = (x + -2)(x + 5)
((6 + -4x) + x(-3 + 2x)) = (x + -2)(x + 5)
(6 + -4x + (-3 * x + 2x * x)) = (x + -2)(x + 5)
(6 + -4x + (-3x + 2x2)) = (x + -2)(x + 5)

Combine like terms: -4x + -3x = -7x
(6 + -7x + 2x2) = (x + -2)(x + 5)

Reorder the terms:
6 + -7x + 2x2 = (-2 + x)(x + 5)

Reorder the terms:
6 + -7x + 2x2 = (-2 + x)(5 + x)

Multiply (-2 + x) * (5 + x)
6 + -7x + 2x2 = (-2(5 + x) + x(5 + x))
6 + -7x + 2x2 = ((5 * -2 + x * -2) + x(5 + x))
6 + -7x + 2x2 = ((-10 + -2x) + x(5 + x))
6 + -7x + 2x2 = (-10 + -2x + (5 * x + x * x))
6 + -7x + 2x2 = (-10 + -2x + (5x + x2))

Combine like terms: -2x + 5x = 3x
6 + -7x + 2x2 = (-10 + 3x + x2)

Solving
6 + -7x + 2x2 = -10 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
6 + 10 + -7x + -3x + 2x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Combine like terms: 6 + 10 = 16
16 + -7x + -3x + 2x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Combine like terms: -7x + -3x = -10x
16 + -10x + 2x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
16 + -10x + 1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Reorder the terms:
16 + -10x + 1x2 = -10 + 10 + 3x + -3x + x2 + -1x2

Combine like terms: -10 + 10 = 0
16 + -10x + 1x2 = 0 + 3x + -3x + x2 + -1x2
16 + -10x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
16 + -10x + 1x2 = 0 + x2 + -1x2
16 + -10x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -10x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -1x) = 0


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 '(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
Solution
x = {2, 8}

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