6x(x+7)=(2x+8)(x+7)

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Solution for 6x(x+7)=(2x+8)(x+7) equation: 


Simplifying
6x(x + 7) = (2x + 8)(x + 7)

Reorder the terms:
6x(7 + x) = (2x + 8)(x + 7)
(7 * 6x + x * 6x) = (2x + 8)(x + 7)
(42x + 6x2) = (2x + 8)(x + 7)

Reorder the terms:
42x + 6x2 = (8 + 2x)(x + 7)

Reorder the terms:
42x + 6x2 = (8 + 2x)(7 + x)

Multiply (8 + 2x) * (7 + x)
42x + 6x2 = (8(7 + x) + 2x * (7 + x))
42x + 6x2 = ((7 * 8 + x * 8) + 2x * (7 + x))
42x + 6x2 = ((56 + 8x) + 2x * (7 + x))
42x + 6x2 = (56 + 8x + (7 * 2x + x * 2x))
42x + 6x2 = (56 + 8x + (14x + 2x2))

Combine like terms: 8x + 14x = 22x
42x + 6x2 = (56 + 22x + 2x2)

Solving
42x + 6x2 = 56 + 22x + 2x2

Solving for variable 'x'.

Reorder the terms:
-56 + 42x + -22x + 6x2 + -2x2 = 56 + 22x + 2x2 + -56 + -22x + -2x2

Combine like terms: 42x + -22x = 20x
-56 + 20x + 6x2 + -2x2 = 56 + 22x + 2x2 + -56 + -22x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-56 + 20x + 4x2 = 56 + 22x + 2x2 + -56 + -22x + -2x2

Reorder the terms:
-56 + 20x + 4x2 = 56 + -56 + 22x + -22x + 2x2 + -2x2

Combine like terms: 56 + -56 = 0
-56 + 20x + 4x2 = 0 + 22x + -22x + 2x2 + -2x2
-56 + 20x + 4x2 = 22x + -22x + 2x2 + -2x2

Combine like terms: 22x + -22x = 0
-56 + 20x + 4x2 = 0 + 2x2 + -2x2
-56 + 20x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-56 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 5x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

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 '(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 = {-7, 2}

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