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

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


Simplifying
x2 + 2x + 3 = (2x + -1)(x + 5)

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

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

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

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

Combine like terms: -1x + 10x = 9x
3 + 2x + x2 = (-5 + 9x + 2x2)

Solving
3 + 2x + x2 = -5 + 9x + 2x2

Solving for variable 'x'.

Reorder the terms:
3 + 5 + 2x + -9x + x2 + -2x2 = -5 + 9x + 2x2 + 5 + -9x + -2x2

Combine like terms: 3 + 5 = 8
8 + 2x + -9x + x2 + -2x2 = -5 + 9x + 2x2 + 5 + -9x + -2x2

Combine like terms: 2x + -9x = -7x
8 + -7x + x2 + -2x2 = -5 + 9x + 2x2 + 5 + -9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
8 + -7x + -1x2 = -5 + 9x + 2x2 + 5 + -9x + -2x2

Reorder the terms:
8 + -7x + -1x2 = -5 + 5 + 9x + -9x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
8 + -7x + -1x2 = 0 + 9x + -9x + 2x2 + -2x2
8 + -7x + -1x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
8 + -7x + -1x2 = 0 + 2x2 + -2x2
8 + -7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -7x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(8 + x) = 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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {1, -8}

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