(x-7)(x+8)=4(x-7)

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Solution for (x-7)(x+8)=4(x-7) equation: 


Simplifying
(x + -7)(x + 8) = 4(x + -7)

Reorder the terms:
(-7 + x)(x + 8) = 4(x + -7)

Reorder the terms:
(-7 + x)(8 + x) = 4(x + -7)

Multiply (-7 + x) * (8 + x)
(-7(8 + x) + x(8 + x)) = 4(x + -7)
((8 * -7 + x * -7) + x(8 + x)) = 4(x + -7)
((-56 + -7x) + x(8 + x)) = 4(x + -7)
(-56 + -7x + (8 * x + x * x)) = 4(x + -7)
(-56 + -7x + (8x + x2)) = 4(x + -7)

Combine like terms: -7x + 8x = 1x
(-56 + 1x + x2) = 4(x + -7)

Reorder the terms:
-56 + 1x + x2 = 4(-7 + x)
-56 + 1x + x2 = (-7 * 4 + x * 4)
-56 + 1x + x2 = (-28 + 4x)

Solving
-56 + 1x + x2 = -28 + 4x

Solving for variable 'x'.

Reorder the terms:
-56 + 28 + 1x + -4x + x2 = -28 + 4x + 28 + -4x

Combine like terms: -56 + 28 = -28
-28 + 1x + -4x + x2 = -28 + 4x + 28 + -4x

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

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

Combine like terms: -28 + 28 = 0
-28 + -3x + x2 = 0 + 4x + -4x
-28 + -3x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-28 + -3x + x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-4, 7}

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