46-(x-4)*(x-4)=37

Solution for 46-(x-4)*(x-4)=37 equation:

Simplifying
46 + -1(x + -4)(x + -4) = 37

Reorder the terms:
46 + -1(-4 + x)(x + -4) = 37

Reorder the terms:
46 + -1(-4 + x)(-4 + x) = 37

Multiply (-4 + x) * (-4 + x)
46 + -1(-4(-4 + x) + x(-4 + x)) = 37
46 + -1((-4 * -4 + x * -4) + x(-4 + x)) = 37
46 + -1((16 + -4x) + x(-4 + x)) = 37
46 + -1(16 + -4x + (-4 * x + x * x)) = 37
46 + -1(16 + -4x + (-4x + x2)) = 37

Combine like terms: -4x + -4x = -8x
46 + -1(16 + -8x + x2) = 37
46 + (16 * -1 + -8x * -1 + x2 * -1) = 37
46 + (-16 + 8x + -1x2) = 37

Combine like terms: 46 + -16 = 30
30 + 8x + -1x2 = 37

Solving
30 + 8x + -1x2 = 37

Solving for variable 'x'.

Reorder the terms:
30 + -37 + 8x + -1x2 = 37 + -37

Combine like terms: 30 + -37 = -7
-7 + 8x + -1x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-7 + 8x + -1x2 = 0

Factor a trinomial.
(-7 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
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 = {7, 1}