0=-4x^2+16x-12

Solution for 0=-4x^2+16x-12 equation:

Simplifying
0 = -4x2 + 16x + -12

Reorder the terms:
0 = -12 + 16x + -4x2

Solving
0 = -12 + 16x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + -16x + 4x2 = -12 + 16x + -4x2 + 12 + -16x + 4x2

Reorder the terms:
12 + -16x + 4x2 = -12 + 12 + 16x + -16x + -4x2 + 4x2

Combine like terms: -12 + 12 = 0
12 + -16x + 4x2 = 0 + 16x + -16x + -4x2 + 4x2
12 + -16x + 4x2 = 16x + -16x + -4x2 + 4x2

Combine like terms: 16x + -16x = 0
12 + -16x + 4x2 = 0 + -4x2 + 4x2
12 + -16x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
12 + -16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -4x + x2) = 0

Factor a trinomial.
4((1 + -1x)(3 + -1x)) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
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 = {1, 3}