(x-7)(x+4)=-4(x-11)

Solution for (x-7)(x+4)=-4(x-11) equation:

Simplifying
(x + -7)(x + 4) = -4(x + -11)

Reorder the terms:
(-7 + x)(x + 4) = -4(x + -11)

Reorder the terms:
(-7 + x)(4 + x) = -4(x + -11)

Multiply (-7 + x) * (4 + x)
(-7(4 + x) + x(4 + x)) = -4(x + -11)
((4 * -7 + x * -7) + x(4 + x)) = -4(x + -11)
((-28 + -7x) + x(4 + x)) = -4(x + -11)
(-28 + -7x + (4 * x + x * x)) = -4(x + -11)
(-28 + -7x + (4x + x2)) = -4(x + -11)

Combine like terms: -7x + 4x = -3x
(-28 + -3x + x2) = -4(x + -11)

Reorder the terms:
-28 + -3x + x2 = -4(-11 + x)
-28 + -3x + x2 = (-11 * -4 + x * -4)
-28 + -3x + x2 = (44 + -4x)

Solving
-28 + -3x + x2 = 44 + -4x

Solving for variable 'x'.

Reorder the terms:
-28 + -44 + -3x + 4x + x2 = 44 + -4x + -44 + 4x

Combine like terms: -28 + -44 = -72
-72 + -3x + 4x + x2 = 44 + -4x + -44 + 4x

Combine like terms: -3x + 4x = 1x
-72 + 1x + x2 = 44 + -4x + -44 + 4x

Reorder the terms:
-72 + 1x + x2 = 44 + -44 + -4x + 4x

Combine like terms: 44 + -44 = 0
-72 + 1x + x2 = 0 + -4x + 4x
-72 + 1x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-72 + 1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-9, 8}