18x^2=39x+84

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Solution for 18x^2=39x+84 equation: 


Simplifying
18x2 = 39x + 84

Reorder the terms:
18x2 = 84 + 39x

Solving
18x2 = 84 + 39x

Solving for variable 'x'.

Reorder the terms:
-84 + -39x + 18x2 = 84 + 39x + -84 + -39x

Reorder the terms:
-84 + -39x + 18x2 = 84 + -84 + 39x + -39x

Combine like terms: 84 + -84 = 0
-84 + -39x + 18x2 = 0 + 39x + -39x
-84 + -39x + 18x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
-84 + -39x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -13x + 6x2) = 0

Factor a trinomial.
3((-4 + -3x)(7 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.333333333, 3.5}

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