(x+1)(x+2)=10x+2

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Solution for (x+1)(x+2)=10x+2 equation: 


Simplifying
(x + 1)(x + 2) = 10x + 2

Reorder the terms:
(1 + x)(x + 2) = 10x + 2

Reorder the terms:
(1 + x)(2 + x) = 10x + 2

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 10x + 2
((2 * 1 + x * 1) + x(2 + x)) = 10x + 2
((2 + 1x) + x(2 + x)) = 10x + 2
(2 + 1x + (2 * x + x * x)) = 10x + 2
(2 + 1x + (2x + x2)) = 10x + 2

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 10x + 2

Reorder the terms:
2 + 3x + x2 = 2 + 10x

Add '-2' to each side of the equation.
2 + 3x + -2 + x2 = 2 + -2 + 10x

Reorder the terms:
2 + -2 + 3x + x2 = 2 + -2 + 10x

Combine like terms: 2 + -2 = 0
0 + 3x + x2 = 2 + -2 + 10x
3x + x2 = 2 + -2 + 10x

Combine like terms: 2 + -2 = 0
3x + x2 = 0 + 10x
3x + x2 = 10x

Solving
3x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
3x + -10x + x2 = 10x + -10x

Combine like terms: 3x + -10x = -7x
-7x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-7x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7
Solution
x = {0, 7}

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