5x(x+2)+8x=-2+3x-8

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Solution for 5x(x+2)+8x=-2+3x-8 equation: 


Simplifying
5x(x + 2) + 8x = -2 + 3x + -8

Reorder the terms:
5x(2 + x) + 8x = -2 + 3x + -8
(2 * 5x + x * 5x) + 8x = -2 + 3x + -8
(10x + 5x2) + 8x = -2 + 3x + -8

Reorder the terms:
10x + 8x + 5x2 = -2 + 3x + -8

Combine like terms: 10x + 8x = 18x
18x + 5x2 = -2 + 3x + -8

Reorder the terms:
18x + 5x2 = -2 + -8 + 3x

Combine like terms: -2 + -8 = -10
18x + 5x2 = -10 + 3x

Solving
18x + 5x2 = -10 + 3x

Solving for variable 'x'.

Reorder the terms:
10 + 18x + -3x + 5x2 = -10 + 3x + 10 + -3x

Combine like terms: 18x + -3x = 15x
10 + 15x + 5x2 = -10 + 3x + 10 + -3x

Reorder the terms:
10 + 15x + 5x2 = -10 + 10 + 3x + -3x

Combine like terms: -10 + 10 = 0
10 + 15x + 5x2 = 0 + 3x + -3x
10 + 15x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
10 + 15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 3x + x2) = 0

Factor a trinomial.
5((2 + x)(1 + x)) = 0

Ignore the factor 5.

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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