(x-5)(x+2)=(x-5)(2x-1)

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Solution for (x-5)(x+2)=(x-5)(2x-1) equation: 


Simplifying
(x + -5)(x + 2) = (x + -5)(2x + -1)

Reorder the terms:
(-5 + x)(x + 2) = (x + -5)(2x + -1)

Reorder the terms:
(-5 + x)(2 + x) = (x + -5)(2x + -1)

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x)) = (x + -5)(2x + -1)
((2 * -5 + x * -5) + x(2 + x)) = (x + -5)(2x + -1)
((-10 + -5x) + x(2 + x)) = (x + -5)(2x + -1)
(-10 + -5x + (2 * x + x * x)) = (x + -5)(2x + -1)
(-10 + -5x + (2x + x2)) = (x + -5)(2x + -1)

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2) = (x + -5)(2x + -1)

Reorder the terms:
-10 + -3x + x2 = (-5 + x)(2x + -1)

Reorder the terms:
-10 + -3x + x2 = (-5 + x)(-1 + 2x)

Multiply (-5 + x) * (-1 + 2x)
-10 + -3x + x2 = (-5(-1 + 2x) + x(-1 + 2x))
-10 + -3x + x2 = ((-1 * -5 + 2x * -5) + x(-1 + 2x))
-10 + -3x + x2 = ((5 + -10x) + x(-1 + 2x))
-10 + -3x + x2 = (5 + -10x + (-1 * x + 2x * x))
-10 + -3x + x2 = (5 + -10x + (-1x + 2x2))

Combine like terms: -10x + -1x = -11x
-10 + -3x + x2 = (5 + -11x + 2x2)

Solving
-10 + -3x + x2 = 5 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + -5 + -3x + 11x + x2 + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Combine like terms: -10 + -5 = -15
-15 + -3x + 11x + x2 + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Combine like terms: -3x + 11x = 8x
-15 + 8x + x2 + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-15 + 8x + -1x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Reorder the terms:
-15 + 8x + -1x2 = 5 + -5 + -11x + 11x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-15 + 8x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2
-15 + 8x + -1x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-15 + 8x + -1x2 = 0 + 2x2 + -2x2
-15 + 8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 8x + -1x2 = 0

Factor a trinomial.
(-5 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {5, 3}

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