6x(x-6)+6=8x-8

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Solution for 6x(x-6)+6=8x-8 equation:


Simplifying
6x(x + -6) + 6 = 8x + -8

Reorder the terms:
6x(-6 + x) + 6 = 8x + -8
(-6 * 6x + x * 6x) + 6 = 8x + -8
(-36x + 6x2) + 6 = 8x + -8

Reorder the terms:
6 + -36x + 6x2 = 8x + -8

Reorder the terms:
6 + -36x + 6x2 = -8 + 8x

Solving
6 + -36x + 6x2 = -8 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + 8 + -36x + -8x + 6x2 = -8 + 8x + 8 + -8x

Combine like terms: 6 + 8 = 14
14 + -36x + -8x + 6x2 = -8 + 8x + 8 + -8x

Combine like terms: -36x + -8x = -44x
14 + -44x + 6x2 = -8 + 8x + 8 + -8x

Reorder the terms:
14 + -44x + 6x2 = -8 + 8 + 8x + -8x

Combine like terms: -8 + 8 = 0
14 + -44x + 6x2 = 0 + 8x + -8x
14 + -44x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
14 + -44x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -22x + 3x2) = 0

Factor a trinomial.
2((1 + -3x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
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
Solution
x = {0.3333333333, 7}

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