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

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


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

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

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

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

Combine like terms: -3x + 10x = 7x
(-15 + 7x + 2x2) = x(x + 5)

Reorder the terms:
-15 + 7x + 2x2 = x(5 + x)
-15 + 7x + 2x2 = (5 * x + x * x)
-15 + 7x + 2x2 = (5x + x2)

Solving
-15 + 7x + 2x2 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
-15 + 7x + -5x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2

Combine like terms: 7x + -5x = 2x
-15 + 2x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2

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

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

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

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

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


Subproblem 1
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

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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