7x=196-28x+x^2

Solution for 7x=196-28x+x^2 equation:

Simplifying
7x = 196 + -28x + x2

Solving
7x = 196 + -28x + x2

Solving for variable 'x'.

Reorder the terms:
-196 + 7x + 28x + -1x2 = 196 + -28x + x2 + -196 + 28x + -1x2

Combine like terms: 7x + 28x = 35x
-196 + 35x + -1x2 = 196 + -28x + x2 + -196 + 28x + -1x2

Reorder the terms:
-196 + 35x + -1x2 = 196 + -196 + -28x + 28x + x2 + -1x2

Combine like terms: 196 + -196 = 0
-196 + 35x + -1x2 = 0 + -28x + 28x + x2 + -1x2
-196 + 35x + -1x2 = -28x + 28x + x2 + -1x2

Combine like terms: -28x + 28x = 0
-196 + 35x + -1x2 = 0 + x2 + -1x2
-196 + 35x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-196 + 35x + -1x2 = 0

Factor a trinomial.
(-28 + x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-28 + x)' equal to zero and attempt to solve:

Simplifying
-28 + x = 0

Solving
-28 + x = 0

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

Add '28' to each side of the equation.
-28 + 28 + x = 0 + 28

Combine like terms: -28 + 28 = 0
0 + x = 0 + 28
x = 0 + 28

Combine like terms: 0 + 28 = 28
x = 28

Simplifying
x = 28
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {28, 7}