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

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


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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: -5 + 5 = 0
2 + -3x + x2 = 0 + -2x + 2x
2 + -3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
2 + -3x + x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

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 = {1, 2}

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