2x(3x+9)+1=.5(2x-8)

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Solution for 2x(3x+9)+1=.5(2x-8) equation: 


Simplifying
2x(3x + 9) + 1 = 0.5(2x + -8)

Reorder the terms:
2x(9 + 3x) + 1 = 0.5(2x + -8)
(9 * 2x + 3x * 2x) + 1 = 0.5(2x + -8)
(18x + 6x2) + 1 = 0.5(2x + -8)

Reorder the terms:
1 + 18x + 6x2 = 0.5(2x + -8)

Reorder the terms:
1 + 18x + 6x2 = 0.5(-8 + 2x)
1 + 18x + 6x2 = (-8 * 0.5 + 2x * 0.5)
1 + 18x + 6x2 = (-4 + 1x)

Solving
1 + 18x + 6x2 = -4 + 1x

Solving for variable 'x'.

Reorder the terms:
1 + 4 + 18x + -1x + 6x2 = -4 + 1x + 4 + -1x

Combine like terms: 1 + 4 = 5
5 + 18x + -1x + 6x2 = -4 + 1x + 4 + -1x

Combine like terms: 18x + -1x = 17x
5 + 17x + 6x2 = -4 + 1x + 4 + -1x

Reorder the terms:
5 + 17x + 6x2 = -4 + 4 + 1x + -1x

Combine like terms: -4 + 4 = 0
5 + 17x + 6x2 = 0 + 1x + -1x
5 + 17x + 6x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
5 + 17x + 6x2 = 0

Factor a trinomial.
(5 + 2x)(1 + 3x) = 0


Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, -0.3333333333}

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