2x^2+7x+5=x(x+3)+17

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Solution for 2x^2+7x+5=x(x+3)+17 equation: 


Simplifying
2x2 + 7x + 5 = x(x + 3) + 17

Reorder the terms:
5 + 7x + 2x2 = x(x + 3) + 17

Reorder the terms:
5 + 7x + 2x2 = x(3 + x) + 17
5 + 7x + 2x2 = (3 * x + x * x) + 17
5 + 7x + 2x2 = (3x + x2) + 17

Reorder the terms:
5 + 7x + 2x2 = 17 + 3x + x2

Solving
5 + 7x + 2x2 = 17 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
5 + -17 + 7x + -3x + 2x2 + -1x2 = 17 + 3x + x2 + -17 + -3x + -1x2

Combine like terms: 5 + -17 = -12
-12 + 7x + -3x + 2x2 + -1x2 = 17 + 3x + x2 + -17 + -3x + -1x2

Combine like terms: 7x + -3x = 4x
-12 + 4x + 2x2 + -1x2 = 17 + 3x + x2 + -17 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-12 + 4x + 1x2 = 17 + 3x + x2 + -17 + -3x + -1x2

Reorder the terms:
-12 + 4x + 1x2 = 17 + -17 + 3x + -3x + x2 + -1x2

Combine like terms: 17 + -17 = 0
-12 + 4x + 1x2 = 0 + 3x + -3x + x2 + -1x2
-12 + 4x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-12 + 4x + 1x2 = 0 + x2 + -1x2
-12 + 4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 4x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 2}

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