180+54x+4x^2=378

Solution for 180+54x+4x^2=378 equation:

Simplifying
180 + 54x + 4x2 = 378

Solving
180 + 54x + 4x2 = 378

Solving for variable 'x'.

Reorder the terms:
180 + -378 + 54x + 4x2 = 378 + -378

Combine like terms: 180 + -378 = -198
-198 + 54x + 4x2 = 378 + -378

Combine like terms: 378 + -378 = 0
-198 + 54x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-99 + 27x + 2x2) = 0

Factor a trinomial.
2((-33 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-33 + -2x)' equal to zero and attempt to solve:

Simplifying
-33 + -2x = 0

Solving
-33 + -2x = 0

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

Add '33' to each side of the equation.
-33 + 33 + -2x = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -2x = 0 + 33
-2x = 0 + 33

Combine like terms: 0 + 33 = 33
-2x = 33

Divide each side by '-2'.
x = -16.5

Simplifying
x = -16.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-16.5, 3}