x(x(-2))=(x^2)+7x+2

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Solution for x(x(-2))=(x^2)+7x+2 equation: 


Simplifying
x(x(-2)) = (x2) + 7x + 2

Reorder the terms for easier multiplication:
x(-2x) = (x2) + 7x + 2

Remove parenthesis around (-2x)
x * -2x = (x2) + 7x + 2

Reorder the terms for easier multiplication:
-2x * x = (x2) + 7x + 2

Multiply x * x
-2x2 = (x2) + 7x + 2
-2x2 = x2 + 7x + 2

Reorder the terms:
-2x2 = 2 + 7x + x2

Solving
-2x2 = 2 + 7x + x2

Solving for variable 'x'.

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

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

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

Combine like terms: 2 + -2 = 0
-2 + -7x + -3x2 = 0 + 7x + -7x + x2 + -1x2
-2 + -7x + -3x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-2 + -7x + -3x2 = 0 + x2 + -1x2
-2 + -7x + -3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + -7x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7x + 3x2) = 0

Factor a trinomial.
-1((2 + x)(1 + 3x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-2, -0.3333333333}

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