(x-1)(x+12)=7x

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Solution for (x-1)(x+12)=7x equation: 


Simplifying
(x + -1)(x + 12) = 7x

Reorder the terms:
(-1 + x)(x + 12) = 7x

Reorder the terms:
(-1 + x)(12 + x) = 7x

Multiply (-1 + x) * (12 + x)
(-1(12 + x) + x(12 + x)) = 7x
((12 * -1 + x * -1) + x(12 + x)) = 7x
((-12 + -1x) + x(12 + x)) = 7x
(-12 + -1x + (12 * x + x * x)) = 7x
(-12 + -1x + (12x + x2)) = 7x

Combine like terms: -1x + 12x = 11x
(-12 + 11x + x2) = 7x

Solving
-12 + 11x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-12 + 11x + -7x + x2 = 7x + -7x

Combine like terms: 11x + -7x = 4x
-12 + 4x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0


Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}

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