3x+5=18x^2+27x-5

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Solution for 3x+5=18x^2+27x-5 equation: 


Simplifying
3x + 5 = 18x2 + 27x + -5

Reorder the terms:
5 + 3x = 18x2 + 27x + -5

Reorder the terms:
5 + 3x = -5 + 27x + 18x2

Solving
5 + 3x = -5 + 27x + 18x2

Solving for variable 'x'.

Reorder the terms:
5 + 5 + 3x + -27x + -18x2 = -5 + 27x + 18x2 + 5 + -27x + -18x2

Combine like terms: 5 + 5 = 10
10 + 3x + -27x + -18x2 = -5 + 27x + 18x2 + 5 + -27x + -18x2

Combine like terms: 3x + -27x = -24x
10 + -24x + -18x2 = -5 + 27x + 18x2 + 5 + -27x + -18x2

Reorder the terms:
10 + -24x + -18x2 = -5 + 5 + 27x + -27x + 18x2 + -18x2

Combine like terms: -5 + 5 = 0
10 + -24x + -18x2 = 0 + 27x + -27x + 18x2 + -18x2
10 + -24x + -18x2 = 27x + -27x + 18x2 + -18x2

Combine like terms: 27x + -27x = 0
10 + -24x + -18x2 = 0 + 18x2 + -18x2
10 + -24x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
10 + -24x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -12x + -9x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0.3333333333, -1.666666667}

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