4x^2-6x+3=57

Solution for 4x^2-6x+3=57 equation:

Simplifying
4x2 + -6x + 3 = 57

Reorder the terms:
3 + -6x + 4x2 = 57

Solving
3 + -6x + 4x2 = 57

Solving for variable 'x'.

Reorder the terms:
3 + -57 + -6x + 4x2 = 57 + -57

Combine like terms: 3 + -57 = -54
-54 + -6x + 4x2 = 57 + -57

Combine like terms: 57 + -57 = 0
-54 + -6x + 4x2 = 0

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

Factor a trinomial.
2((-3 + -1x)(9 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 4.5}