(x-7)(x+4)=-(x+4)

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Solution for (x-7)(x+4)=-(x+4) equation: 


Simplifying
(x + -7)(x + 4) = -1(x + 4)

Reorder the terms:
(-7 + x)(x + 4) = -1(x + 4)

Reorder the terms:
(-7 + x)(4 + x) = -1(x + 4)

Multiply (-7 + x) * (4 + x)
(-7(4 + x) + x(4 + x)) = -1(x + 4)
((4 * -7 + x * -7) + x(4 + x)) = -1(x + 4)
((-28 + -7x) + x(4 + x)) = -1(x + 4)
(-28 + -7x + (4 * x + x * x)) = -1(x + 4)
(-28 + -7x + (4x + x2)) = -1(x + 4)

Combine like terms: -7x + 4x = -3x
(-28 + -3x + x2) = -1(x + 4)

Reorder the terms:
-28 + -3x + x2 = -1(4 + x)
-28 + -3x + x2 = (4 * -1 + x * -1)
-28 + -3x + x2 = (-4 + -1x)

Solving
-28 + -3x + x2 = -4 + -1x

Solving for variable 'x'.

Reorder the terms:
-28 + 4 + -3x + x + x2 = -4 + -1x + 4 + x

Combine like terms: -28 + 4 = -24
-24 + -3x + x + x2 = -4 + -1x + 4 + x

Combine like terms: -3x + x = -2x
-24 + -2x + x2 = -4 + -1x + 4 + x

Reorder the terms:
-24 + -2x + x2 = -4 + 4 + -1x + x

Combine like terms: -4 + 4 = 0
-24 + -2x + x2 = 0 + -1x + x
-24 + -2x + x2 = -1x + x

Combine like terms: -1x + x = 0
-24 + -2x + x2 = 0

Factor a trinomial.
(-4 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4, 6}

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