x^2+4x-40=10x+15

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Solution for x^2+4x-40=10x+15 equation: 


Simplifying
x2 + 4x + -40 = 10x + 15

Reorder the terms:
-40 + 4x + x2 = 10x + 15

Reorder the terms:
-40 + 4x + x2 = 15 + 10x

Solving
-40 + 4x + x2 = 15 + 10x

Solving for variable 'x'.

Reorder the terms:
-40 + -15 + 4x + -10x + x2 = 15 + 10x + -15 + -10x

Combine like terms: -40 + -15 = -55
-55 + 4x + -10x + x2 = 15 + 10x + -15 + -10x

Combine like terms: 4x + -10x = -6x
-55 + -6x + x2 = 15 + 10x + -15 + -10x

Reorder the terms:
-55 + -6x + x2 = 15 + -15 + 10x + -10x

Combine like terms: 15 + -15 = 0
-55 + -6x + x2 = 0 + 10x + -10x
-55 + -6x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-55 + -6x + x2 = 0

Factor a trinomial.
(-5 + -1x)(11 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-5, 11}

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