28(x-7)-(x+6)=(x+6)(x-7)

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Solution for 28(x-7)-(x+6)=(x+6)(x-7) equation: 


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

Reorder the terms:
28(-7 + x) + -1(x + 6) = (x + 6)(x + -7)
(-7 * 28 + x * 28) + -1(x + 6) = (x + 6)(x + -7)
(-196 + 28x) + -1(x + 6) = (x + 6)(x + -7)

Reorder the terms:
-196 + 28x + -1(6 + x) = (x + 6)(x + -7)
-196 + 28x + (6 * -1 + x * -1) = (x + 6)(x + -7)
-196 + 28x + (-6 + -1x) = (x + 6)(x + -7)

Reorder the terms:
-196 + -6 + 28x + -1x = (x + 6)(x + -7)

Combine like terms: -196 + -6 = -202
-202 + 28x + -1x = (x + 6)(x + -7)

Combine like terms: 28x + -1x = 27x
-202 + 27x = (x + 6)(x + -7)

Reorder the terms:
-202 + 27x = (6 + x)(x + -7)

Reorder the terms:
-202 + 27x = (6 + x)(-7 + x)

Multiply (6 + x) * (-7 + x)
-202 + 27x = (6(-7 + x) + x(-7 + x))
-202 + 27x = ((-7 * 6 + x * 6) + x(-7 + x))
-202 + 27x = ((-42 + 6x) + x(-7 + x))
-202 + 27x = (-42 + 6x + (-7 * x + x * x))
-202 + 27x = (-42 + 6x + (-7x + x2))

Combine like terms: 6x + -7x = -1x
-202 + 27x = (-42 + -1x + x2)

Solving
-202 + 27x = -42 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-202 + 42 + 27x + x + -1x2 = -42 + -1x + x2 + 42 + x + -1x2

Combine like terms: -202 + 42 = -160
-160 + 27x + x + -1x2 = -42 + -1x + x2 + 42 + x + -1x2

Combine like terms: 27x + x = 28x
-160 + 28x + -1x2 = -42 + -1x + x2 + 42 + x + -1x2

Reorder the terms:
-160 + 28x + -1x2 = -42 + 42 + -1x + x + x2 + -1x2

Combine like terms: -42 + 42 = 0
-160 + 28x + -1x2 = 0 + -1x + x + x2 + -1x2
-160 + 28x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-160 + 28x + -1x2 = 0 + x2 + -1x2
-160 + 28x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-160 + 28x + -1x2 = 0

Factor a trinomial.
(-20 + x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {20, 8}

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