(x-7)(x+3)=-7(x-1)

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Solution for (x-7)(x+3)=-7(x-1) equation: 


Simplifying
(x + -7)(x + 3) = -7(x + -1)

Reorder the terms:
(-7 + x)(x + 3) = -7(x + -1)

Reorder the terms:
(-7 + x)(3 + x) = -7(x + -1)

Multiply (-7 + x) * (3 + x)
(-7(3 + x) + x(3 + x)) = -7(x + -1)
((3 * -7 + x * -7) + x(3 + x)) = -7(x + -1)
((-21 + -7x) + x(3 + x)) = -7(x + -1)
(-21 + -7x + (3 * x + x * x)) = -7(x + -1)
(-21 + -7x + (3x + x2)) = -7(x + -1)

Combine like terms: -7x + 3x = -4x
(-21 + -4x + x2) = -7(x + -1)

Reorder the terms:
-21 + -4x + x2 = -7(-1 + x)
-21 + -4x + x2 = (-1 * -7 + x * -7)
-21 + -4x + x2 = (7 + -7x)

Solving
-21 + -4x + x2 = 7 + -7x

Solving for variable 'x'.

Reorder the terms:
-21 + -7 + -4x + 7x + x2 = 7 + -7x + -7 + 7x

Combine like terms: -21 + -7 = -28
-28 + -4x + 7x + x2 = 7 + -7x + -7 + 7x

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

Reorder the terms:
-28 + 3x + x2 = 7 + -7 + -7x + 7x

Combine like terms: 7 + -7 = 0
-28 + 3x + x2 = 0 + -7x + 7x
-28 + 3x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-7, 4}

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