5x(x-1)-4x(x+4)=-110

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Solution for 5x(x-1)-4x(x+4)=-110 equation: 


Simplifying
5x(x + -1) + -4x(x + 4) = -110

Reorder the terms:
5x(-1 + x) + -4x(x + 4) = -110
(-1 * 5x + x * 5x) + -4x(x + 4) = -110
(-5x + 5x2) + -4x(x + 4) = -110

Reorder the terms:
-5x + 5x2 + -4x(4 + x) = -110
-5x + 5x2 + (4 * -4x + x * -4x) = -110
-5x + 5x2 + (-16x + -4x2) = -110

Reorder the terms:
-5x + -16x + 5x2 + -4x2 = -110

Combine like terms: -5x + -16x = -21x
-21x + 5x2 + -4x2 = -110

Combine like terms: 5x2 + -4x2 = 1x2
-21x + 1x2 = -110

Solving
-21x + 1x2 = -110

Solving for variable 'x'.

Reorder the terms:
110 + -21x + 1x2 = -110 + 110

Combine like terms: -110 + 110 = 0
110 + -21x + 1x2 = 0

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


Subproblem 1
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

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 = {10, 11}

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