2x^2+15x+31=(x+5)(x+5)

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Solution for 2x^2+15x+31=(x+5)(x+5) equation: 


Simplifying
2x2 + 15x + 31 = (x + 5)(x + 5)

Reorder the terms:
31 + 15x + 2x2 = (x + 5)(x + 5)

Reorder the terms:
31 + 15x + 2x2 = (5 + x)(x + 5)

Reorder the terms:
31 + 15x + 2x2 = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
31 + 15x + 2x2 = (5(5 + x) + x(5 + x))
31 + 15x + 2x2 = ((5 * 5 + x * 5) + x(5 + x))
31 + 15x + 2x2 = ((25 + 5x) + x(5 + x))
31 + 15x + 2x2 = (25 + 5x + (5 * x + x * x))
31 + 15x + 2x2 = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
31 + 15x + 2x2 = (25 + 10x + x2)

Solving
31 + 15x + 2x2 = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
31 + -25 + 15x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 31 + -25 = 6
6 + 15x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 15x + -10x = 5x
6 + 5x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
6 + 5x + 1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
6 + 5x + 1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
6 + 5x + 1x2 = 0 + 10x + -10x + x2 + -1x2
6 + 5x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
6 + 5x + 1x2 = 0 + x2 + -1x2
6 + 5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + 1x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0


Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-3, -2}

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