2(x+1)(x+7)=54

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Solution for 2(x+1)(x+7)=54 equation: 


Simplifying
2(x + 1)(x + 7) = 54

Reorder the terms:
2(1 + x)(x + 7) = 54

Reorder the terms:
2(1 + x)(7 + x) = 54

Multiply (1 + x) * (7 + x)
2(1(7 + x) + x(7 + x)) = 54
2((7 * 1 + x * 1) + x(7 + x)) = 54
2((7 + 1x) + x(7 + x)) = 54
2(7 + 1x + (7 * x + x * x)) = 54
2(7 + 1x + (7x + x2)) = 54

Combine like terms: 1x + 7x = 8x
2(7 + 8x + x2) = 54
(7 * 2 + 8x * 2 + x2 * 2) = 54
(14 + 16x + 2x2) = 54

Solving
14 + 16x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
14 + -54 + 16x + 2x2 = 54 + -54

Combine like terms: 14 + -54 = -40
-40 + 16x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-40 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 8x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-10, 2}

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