25-5x=x^2+3x-23

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Solution for 25-5x=x^2+3x-23 equation: 


Simplifying
25 + -5x = x2 + 3x + -23

Reorder the terms:
25 + -5x = -23 + 3x + x2

Solving
25 + -5x = -23 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
25 + 23 + -5x + -3x + -1x2 = -23 + 3x + x2 + 23 + -3x + -1x2

Combine like terms: 25 + 23 = 48
48 + -5x + -3x + -1x2 = -23 + 3x + x2 + 23 + -3x + -1x2

Combine like terms: -5x + -3x = -8x
48 + -8x + -1x2 = -23 + 3x + x2 + 23 + -3x + -1x2

Reorder the terms:
48 + -8x + -1x2 = -23 + 23 + 3x + -3x + x2 + -1x2

Combine like terms: -23 + 23 = 0
48 + -8x + -1x2 = 0 + 3x + -3x + x2 + -1x2
48 + -8x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
48 + -8x + -1x2 = 0 + x2 + -1x2
48 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -8x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(12 + x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {4, -12}

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