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

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


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

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

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

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

Multiply (3 + x) * (-5 + x)
-10x + 2x2 = (3(-5 + x) + x(-5 + x))
-10x + 2x2 = ((-5 * 3 + x * 3) + x(-5 + x))
-10x + 2x2 = ((-15 + 3x) + x(-5 + x))
-10x + 2x2 = (-15 + 3x + (-5 * x + x * x))
-10x + 2x2 = (-15 + 3x + (-5x + x2))

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

Solving
-10x + 2x2 = -15 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
15 + -10x + 2x + 2x2 + -1x2 = -15 + -2x + x2 + 15 + 2x + -1x2

Combine like terms: -10x + 2x = -8x
15 + -8x + 2x2 + -1x2 = -15 + -2x + x2 + 15 + 2x + -1x2

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

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

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

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

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

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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

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