(x+6)(x-2)+7=0

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Solution for (x+6)(x-2)+7=0 equation: 


Simplifying
(x + 6)(x + -2) + 7 = 0

Reorder the terms:
(6 + x)(x + -2) + 7 = 0

Reorder the terms:
(6 + x)(-2 + x) + 7 = 0

Multiply (6 + x) * (-2 + x)
(6(-2 + x) + x(-2 + x)) + 7 = 0
((-2 * 6 + x * 6) + x(-2 + x)) + 7 = 0
((-12 + 6x) + x(-2 + x)) + 7 = 0
(-12 + 6x + (-2 * x + x * x)) + 7 = 0
(-12 + 6x + (-2x + x2)) + 7 = 0

Combine like terms: 6x + -2x = 4x
(-12 + 4x + x2) + 7 = 0

Reorder the terms:
-12 + 7 + 4x + x2 = 0

Combine like terms: -12 + 7 = -5
-5 + 4x + x2 = 0

Solving
-5 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 1}

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