3(x-4)+x^2=28

Solution for 3(x-4)+x^2=28 equation:

Simplifying
3(x + -4) + x2 = 28

Reorder the terms:
3(-4 + x) + x2 = 28
(-4 * 3 + x * 3) + x2 = 28
(-12 + 3x) + x2 = 28

Solving
-12 + 3x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
-12 + -28 + 3x + x2 = 28 + -28

Combine like terms: -12 + -28 = -40
-40 + 3x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-40 + 3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-8, 5}