(x+6)(x-7)=(2x+5)(x-7)

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Solution for (x+6)(x-7)=(2x+5)(x-7) equation: 


Simplifying
(x + 6)(x + -7) = (2x + 5)(x + -7)

Reorder the terms:
(6 + x)(x + -7) = (2x + 5)(x + -7)

Reorder the terms:
(6 + x)(-7 + x) = (2x + 5)(x + -7)

Multiply (6 + x) * (-7 + x)
(6(-7 + x) + x(-7 + x)) = (2x + 5)(x + -7)
((-7 * 6 + x * 6) + x(-7 + x)) = (2x + 5)(x + -7)
((-42 + 6x) + x(-7 + x)) = (2x + 5)(x + -7)
(-42 + 6x + (-7 * x + x * x)) = (2x + 5)(x + -7)
(-42 + 6x + (-7x + x2)) = (2x + 5)(x + -7)

Combine like terms: 6x + -7x = -1x
(-42 + -1x + x2) = (2x + 5)(x + -7)

Reorder the terms:
-42 + -1x + x2 = (5 + 2x)(x + -7)

Reorder the terms:
-42 + -1x + x2 = (5 + 2x)(-7 + x)

Multiply (5 + 2x) * (-7 + x)
-42 + -1x + x2 = (5(-7 + x) + 2x * (-7 + x))
-42 + -1x + x2 = ((-7 * 5 + x * 5) + 2x * (-7 + x))
-42 + -1x + x2 = ((-35 + 5x) + 2x * (-7 + x))
-42 + -1x + x2 = (-35 + 5x + (-7 * 2x + x * 2x))
-42 + -1x + x2 = (-35 + 5x + (-14x + 2x2))

Combine like terms: 5x + -14x = -9x
-42 + -1x + x2 = (-35 + -9x + 2x2)

Solving
-42 + -1x + x2 = -35 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-42 + 35 + -1x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Combine like terms: -42 + 35 = -7
-7 + -1x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Combine like terms: -1x + 9x = 8x
-7 + 8x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-7 + 8x + -1x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Reorder the terms:
-7 + 8x + -1x2 = -35 + 35 + -9x + 9x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
-7 + 8x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2
-7 + 8x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-7 + 8x + -1x2 = 0 + 2x2 + -2x2
-7 + 8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 8x + -1x2 = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {7, 1}

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