x^2+5x=4x+110

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Solution for x^2+5x=4x+110 equation: 


Simplifying
x2 + 5x = 4x + 110

Reorder the terms:
5x + x2 = 4x + 110

Reorder the terms:
5x + x2 = 110 + 4x

Solving
5x + x2 = 110 + 4x

Solving for variable 'x'.

Reorder the terms:
-110 + 5x + -4x + x2 = 110 + 4x + -110 + -4x

Combine like terms: 5x + -4x = 1x
-110 + 1x + x2 = 110 + 4x + -110 + -4x

Reorder the terms:
-110 + 1x + x2 = 110 + -110 + 4x + -4x

Combine like terms: 110 + -110 = 0
-110 + 1x + x2 = 0 + 4x + -4x
-110 + 1x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-110 + 1x + x2 = 0

Factor a trinomial.
(-11 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-11, 10}

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