3x(x+2)+x=2x(x+10)+5(x-10)-27

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Solution for 3x(x+2)+x=2x(x+10)+5(x-10)-27 equation: 


Simplifying
3x(x + 2) + x = 2x(x + 10) + 5(x + -10) + -27

Reorder the terms:
3x(2 + x) + x = 2x(x + 10) + 5(x + -10) + -27
(2 * 3x + x * 3x) + x = 2x(x + 10) + 5(x + -10) + -27
(6x + 3x2) + x = 2x(x + 10) + 5(x + -10) + -27

Reorder the terms:
6x + x + 3x2 = 2x(x + 10) + 5(x + -10) + -27

Combine like terms: 6x + x = 7x
7x + 3x2 = 2x(x + 10) + 5(x + -10) + -27

Reorder the terms:
7x + 3x2 = 2x(10 + x) + 5(x + -10) + -27
7x + 3x2 = (10 * 2x + x * 2x) + 5(x + -10) + -27
7x + 3x2 = (20x + 2x2) + 5(x + -10) + -27

Reorder the terms:
7x + 3x2 = 20x + 2x2 + 5(-10 + x) + -27
7x + 3x2 = 20x + 2x2 + (-10 * 5 + x * 5) + -27
7x + 3x2 = 20x + 2x2 + (-50 + 5x) + -27

Reorder the terms:
7x + 3x2 = -50 + -27 + 20x + 5x + 2x2

Combine like terms: -50 + -27 = -77
7x + 3x2 = -77 + 20x + 5x + 2x2

Combine like terms: 20x + 5x = 25x
7x + 3x2 = -77 + 25x + 2x2

Solving
7x + 3x2 = -77 + 25x + 2x2

Solving for variable 'x'.

Reorder the terms:
77 + 7x + -25x + 3x2 + -2x2 = -77 + 25x + 2x2 + 77 + -25x + -2x2

Combine like terms: 7x + -25x = -18x
77 + -18x + 3x2 + -2x2 = -77 + 25x + 2x2 + 77 + -25x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
77 + -18x + 1x2 = -77 + 25x + 2x2 + 77 + -25x + -2x2

Reorder the terms:
77 + -18x + 1x2 = -77 + 77 + 25x + -25x + 2x2 + -2x2

Combine like terms: -77 + 77 = 0
77 + -18x + 1x2 = 0 + 25x + -25x + 2x2 + -2x2
77 + -18x + 1x2 = 25x + -25x + 2x2 + -2x2

Combine like terms: 25x + -25x = 0
77 + -18x + 1x2 = 0 + 2x2 + -2x2
77 + -18x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
77 + -18x + 1x2 = 0

Factor a trinomial.
(7 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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 = {7, 11}

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