(x-7)(x+1)=20

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Solution for (x-7)(x+1)=20 equation: 


Simplifying
(x + -7)(x + 1) = 20

Reorder the terms:
(-7 + x)(x + 1) = 20

Reorder the terms:
(-7 + x)(1 + x) = 20

Multiply (-7 + x) * (1 + x)
(-7(1 + x) + x(1 + x)) = 20
((1 * -7 + x * -7) + x(1 + x)) = 20
((-7 + -7x) + x(1 + x)) = 20
(-7 + -7x + (1 * x + x * x)) = 20
(-7 + -7x + (1x + x2)) = 20

Combine like terms: -7x + 1x = -6x
(-7 + -6x + x2) = 20

Solving
-7 + -6x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-7 + -20 + -6x + x2 = 20 + -20

Combine like terms: -7 + -20 = -27
-27 + -6x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-27 + -6x + x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-3, 9}

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