4x*x-(x*x-6x+9)=0

Solution for 4x*x-(x*x-6x+9)=0 equation:

Simplifying
4x * x + -1(x * x + -6x + 9) = 0

Multiply x * x
4x2 + -1(x * x + -6x + 9) = 0

Multiply x * x
4x2 + -1(x2 + -6x + 9) = 0

Reorder the terms:
4x2 + -1(9 + -6x + x2) = 0
4x2 + (9 * -1 + -6x * -1 + x2 * -1) = 0
4x2 + (-9 + 6x + -1x2) = 0

Reorder the terms:
-9 + 6x + 4x2 + -1x2 = 0

Combine like terms: 4x2 + -1x2 = 3x2
-9 + 6x + 3x2 = 0

Solving
-9 + 6x + 3x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
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 '(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
Solution
x = {-3, 1}