14x+40=x^2+20x

Solution for 14x+40=x^2+20x equation:

Simplifying
14x + 40 = x2 + 20x

Reorder the terms:
40 + 14x = x2 + 20x

Reorder the terms:
40 + 14x = 20x + x2

Solving
40 + 14x = 20x + x2

Solving for variable 'x'.

Combine like terms: 14x + -20x = -6x
40 + -6x + -1x2 = 20x + x2 + -20x + -1x2

Reorder the terms:
40 + -6x + -1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
40 + -6x + -1x2 = 0 + x2 + -1x2
40 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + -6x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(10 + 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {4, -10}