6x=7x^2+9x-54

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Solution for 6x=7x^2+9x-54 equation: 


Simplifying
6x = 7x2 + 9x + -54

Reorder the terms:
6x = -54 + 9x + 7x2

Solving
6x = -54 + 9x + 7x2

Solving for variable 'x'.

Reorder the terms:
54 + 6x + -9x + -7x2 = -54 + 9x + 7x2 + 54 + -9x + -7x2

Combine like terms: 6x + -9x = -3x
54 + -3x + -7x2 = -54 + 9x + 7x2 + 54 + -9x + -7x2

Reorder the terms:
54 + -3x + -7x2 = -54 + 54 + 9x + -9x + 7x2 + -7x2

Combine like terms: -54 + 54 = 0
54 + -3x + -7x2 = 0 + 9x + -9x + 7x2 + -7x2
54 + -3x + -7x2 = 9x + -9x + 7x2 + -7x2

Combine like terms: 9x + -9x = 0
54 + -3x + -7x2 = 0 + 7x2 + -7x2
54 + -3x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
54 + -3x + -7x2 = 0

Factor a trinomial.
(18 + -7x)(3 + x) = 0


Subproblem 1
Set the factor '(18 + -7x)' equal to zero and attempt to solve:

Simplifying
18 + -7x = 0

Solving
18 + -7x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -7x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -7x = 0 + -18
-7x = 0 + -18

Combine like terms: 0 + -18 = -18
-7x = -18

Divide each side by '-7'.
x = 2.571428571

Simplifying
x = 2.571428571

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {2.571428571, -3}

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