(x+3)(x-5)=(2x+1)(x-5)

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Solution for (x+3)(x-5)=(2x+1)(x-5) equation: 


Simplifying
(x + 3)(x + -5) = (2x + 1)(x + -5)

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

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

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) = (2x + 1)(x + -5)
((-5 * 3 + x * 3) + x(-5 + x)) = (2x + 1)(x + -5)
((-15 + 3x) + x(-5 + x)) = (2x + 1)(x + -5)
(-15 + 3x + (-5 * x + x * x)) = (2x + 1)(x + -5)
(-15 + 3x + (-5x + x2)) = (2x + 1)(x + -5)

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) = (2x + 1)(x + -5)

Reorder the terms:
-15 + -2x + x2 = (1 + 2x)(x + -5)

Reorder the terms:
-15 + -2x + x2 = (1 + 2x)(-5 + x)

Multiply (1 + 2x) * (-5 + x)
-15 + -2x + x2 = (1(-5 + x) + 2x * (-5 + x))
-15 + -2x + x2 = ((-5 * 1 + x * 1) + 2x * (-5 + x))
-15 + -2x + x2 = ((-5 + 1x) + 2x * (-5 + x))
-15 + -2x + x2 = (-5 + 1x + (-5 * 2x + x * 2x))
-15 + -2x + x2 = (-5 + 1x + (-10x + 2x2))

Combine like terms: 1x + -10x = -9x
-15 + -2x + x2 = (-5 + -9x + 2x2)

Solving
-15 + -2x + x2 = -5 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-15 + 5 + -2x + 9x + x2 + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2

Combine like terms: -15 + 5 = -10
-10 + -2x + 9x + x2 + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2

Combine like terms: -2x + 9x = 7x
-10 + 7x + x2 + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-10 + 7x + -1x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2

Reorder the terms:
-10 + 7x + -1x2 = -5 + 5 + -9x + 9x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
-10 + 7x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2
-10 + 7x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-10 + 7x + -1x2 = 0 + 2x2 + -2x2
-10 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 7x + -1x2 = 0

Factor a trinomial.
(-5 + x)(2 + -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 '(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
Solution
x = {5, 2}

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