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

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Solution for x(x-1)=-4(x-7) equation: 


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

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

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

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

Solving for variable 'x'.

Reorder the terms:
-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.
(-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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