2x^2+16x+31=(x+4)(x+4)

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Solution for 2x^2+16x+31=(x+4)(x+4) equation: 


Simplifying
2x2 + 16x + 31 = (x + 4)(x + 4)

Reorder the terms:
31 + 16x + 2x2 = (x + 4)(x + 4)

Reorder the terms:
31 + 16x + 2x2 = (4 + x)(x + 4)

Reorder the terms:
31 + 16x + 2x2 = (4 + x)(4 + x)

Multiply (4 + x) * (4 + x)
31 + 16x + 2x2 = (4(4 + x) + x(4 + x))
31 + 16x + 2x2 = ((4 * 4 + x * 4) + x(4 + x))
31 + 16x + 2x2 = ((16 + 4x) + x(4 + x))
31 + 16x + 2x2 = (16 + 4x + (4 * x + x * x))
31 + 16x + 2x2 = (16 + 4x + (4x + x2))

Combine like terms: 4x + 4x = 8x
31 + 16x + 2x2 = (16 + 8x + x2)

Solving
31 + 16x + 2x2 = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
31 + -16 + 16x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 31 + -16 = 15
15 + 16x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 16x + -8x = 8x
15 + 8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
15 + 8x + 1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
15 + 8x + 1x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
15 + 8x + 1x2 = 0 + 8x + -8x + x2 + -1x2
15 + 8x + 1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
15 + 8x + 1x2 = 0 + x2 + -1x2
15 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 1x2 = 0

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


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, -3}

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