(x+2)(x+5)+2x=2x+10+4x+4

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Solution for (x+2)(x+5)+2x=2x+10+4x+4 equation: 


Simplifying
(x + 2)(x + 5) + 2x = 2x + 10 + 4x + 4

Reorder the terms:
(2 + x)(x + 5) + 2x = 2x + 10 + 4x + 4

Reorder the terms:
(2 + x)(5 + x) + 2x = 2x + 10 + 4x + 4

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) + 2x = 2x + 10 + 4x + 4
((5 * 2 + x * 2) + x(5 + x)) + 2x = 2x + 10 + 4x + 4
((10 + 2x) + x(5 + x)) + 2x = 2x + 10 + 4x + 4
(10 + 2x + (5 * x + x * x)) + 2x = 2x + 10 + 4x + 4
(10 + 2x + (5x + x2)) + 2x = 2x + 10 + 4x + 4

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) + 2x = 2x + 10 + 4x + 4

Reorder the terms:
10 + 7x + 2x + x2 = 2x + 10 + 4x + 4

Combine like terms: 7x + 2x = 9x
10 + 9x + x2 = 2x + 10 + 4x + 4

Reorder the terms:
10 + 9x + x2 = 10 + 4 + 2x + 4x

Combine like terms: 10 + 4 = 14
10 + 9x + x2 = 14 + 2x + 4x

Combine like terms: 2x + 4x = 6x
10 + 9x + x2 = 14 + 6x

Solving
10 + 9x + x2 = 14 + 6x

Solving for variable 'x'.

Reorder the terms:
10 + -14 + 9x + -6x + x2 = 14 + 6x + -14 + -6x

Combine like terms: 10 + -14 = -4
-4 + 9x + -6x + x2 = 14 + 6x + -14 + -6x

Combine like terms: 9x + -6x = 3x
-4 + 3x + x2 = 14 + 6x + -14 + -6x

Reorder the terms:
-4 + 3x + x2 = 14 + -14 + 6x + -6x

Combine like terms: 14 + -14 = 0
-4 + 3x + x2 = 0 + 6x + -6x
-4 + 3x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-4 + 3x + x2 = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}

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