3x(x-7)=(2x+8)(x-7)

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Solution for 3x(x-7)=(2x+8)(x-7) equation: 


Simplifying
3x(x + -7) = (2x + 8)(x + -7)

Reorder the terms:
3x(-7 + x) = (2x + 8)(x + -7)
(-7 * 3x + x * 3x) = (2x + 8)(x + -7)
(-21x + 3x2) = (2x + 8)(x + -7)

Reorder the terms:
-21x + 3x2 = (8 + 2x)(x + -7)

Reorder the terms:
-21x + 3x2 = (8 + 2x)(-7 + x)

Multiply (8 + 2x) * (-7 + x)
-21x + 3x2 = (8(-7 + x) + 2x * (-7 + x))
-21x + 3x2 = ((-7 * 8 + x * 8) + 2x * (-7 + x))
-21x + 3x2 = ((-56 + 8x) + 2x * (-7 + x))
-21x + 3x2 = (-56 + 8x + (-7 * 2x + x * 2x))
-21x + 3x2 = (-56 + 8x + (-14x + 2x2))

Combine like terms: 8x + -14x = -6x
-21x + 3x2 = (-56 + -6x + 2x2)

Solving
-21x + 3x2 = -56 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
56 + -21x + 6x + 3x2 + -2x2 = -56 + -6x + 2x2 + 56 + 6x + -2x2

Combine like terms: -21x + 6x = -15x
56 + -15x + 3x2 + -2x2 = -56 + -6x + 2x2 + 56 + 6x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
56 + -15x + 1x2 = -56 + -6x + 2x2 + 56 + 6x + -2x2

Reorder the terms:
56 + -15x + 1x2 = -56 + 56 + -6x + 6x + 2x2 + -2x2

Combine like terms: -56 + 56 = 0
56 + -15x + 1x2 = 0 + -6x + 6x + 2x2 + -2x2
56 + -15x + 1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
56 + -15x + 1x2 = 0 + 2x2 + -2x2
56 + -15x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
56 + -15x + 1x2 = 0

Factor a trinomial.
(7 + -1x)(8 + -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 '(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 = {7, 8}

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