6x+54=4x^2

Solution for 6x+54=4x^2 equation:

Simplifying
6x + 54 = 4x2

Reorder the terms:
54 + 6x = 4x2

Solving
54 + 6x = 4x2

Solving for variable 'x'.

Combine like terms: 4x2 + -4x2 = 0
54 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 3x + -2x2) = 0

Factor a trinomial.
2((9 + -2x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
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 = {4.5, -3}