(x+6)(x-7)=(2x+1)(x-7)

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Solution for (x+6)(x-7)=(2x+1)(x-7) equation: 


Simplifying
(x + 6)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(6 + x)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(6 + x)(-7 + x) = (2x + 1)(x + -7)

Multiply (6 + x) * (-7 + x)
(6(-7 + x) + x(-7 + x)) = (2x + 1)(x + -7)
((-7 * 6 + x * 6) + x(-7 + x)) = (2x + 1)(x + -7)
((-42 + 6x) + x(-7 + x)) = (2x + 1)(x + -7)
(-42 + 6x + (-7 * x + x * x)) = (2x + 1)(x + -7)
(-42 + 6x + (-7x + x2)) = (2x + 1)(x + -7)

Combine like terms: 6x + -7x = -1x
(-42 + -1x + x2) = (2x + 1)(x + -7)

Reorder the terms:
-42 + -1x + x2 = (1 + 2x)(x + -7)

Reorder the terms:
-42 + -1x + x2 = (1 + 2x)(-7 + x)

Multiply (1 + 2x) * (-7 + x)
-42 + -1x + x2 = (1(-7 + x) + 2x * (-7 + x))
-42 + -1x + x2 = ((-7 * 1 + x * 1) + 2x * (-7 + x))
-42 + -1x + x2 = ((-7 + 1x) + 2x * (-7 + x))
-42 + -1x + x2 = (-7 + 1x + (-7 * 2x + x * 2x))
-42 + -1x + x2 = (-7 + 1x + (-14x + 2x2))

Combine like terms: 1x + -14x = -13x
-42 + -1x + x2 = (-7 + -13x + 2x2)

Solving
-42 + -1x + x2 = -7 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
-42 + 7 + -1x + 13x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: -42 + 7 = -35
-35 + -1x + 13x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: -1x + 13x = 12x
-35 + 12x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-35 + 12x + -1x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Reorder the terms:
-35 + 12x + -1x2 = -7 + 7 + -13x + 13x + 2x2 + -2x2

Combine like terms: -7 + 7 = 0
-35 + 12x + -1x2 = 0 + -13x + 13x + 2x2 + -2x2
-35 + 12x + -1x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
-35 + 12x + -1x2 = 0 + 2x2 + -2x2
-35 + 12x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-35 + 12x + -1x2 = 0

Factor a trinomial.
(-7 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {7, 5}

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