6x(x-8)+18=4(x-7)

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Solution for 6x(x-8)+18=4(x-7) equation: 


Simplifying
6x(x + -8) + 18 = 4(x + -7)

Reorder the terms:
6x(-8 + x) + 18 = 4(x + -7)
(-8 * 6x + x * 6x) + 18 = 4(x + -7)
(-48x + 6x2) + 18 = 4(x + -7)

Reorder the terms:
18 + -48x + 6x2 = 4(x + -7)

Reorder the terms:
18 + -48x + 6x2 = 4(-7 + x)
18 + -48x + 6x2 = (-7 * 4 + x * 4)
18 + -48x + 6x2 = (-28 + 4x)

Solving
18 + -48x + 6x2 = -28 + 4x

Solving for variable 'x'.

Reorder the terms:
18 + 28 + -48x + -4x + 6x2 = -28 + 4x + 28 + -4x

Combine like terms: 18 + 28 = 46
46 + -48x + -4x + 6x2 = -28 + 4x + 28 + -4x

Combine like terms: -48x + -4x = -52x
46 + -52x + 6x2 = -28 + 4x + 28 + -4x

Reorder the terms:
46 + -52x + 6x2 = -28 + 28 + 4x + -4x

Combine like terms: -28 + 28 = 0
46 + -52x + 6x2 = 0 + 4x + -4x
46 + -52x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
46 + -52x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + -26x + 3x2) = 0

Factor a trinomial.
2((1 + -1x)(23 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(23 + -3x)' equal to zero and attempt to solve:

Simplifying
23 + -3x = 0

Solving
23 + -3x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -3x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -3x = 0 + -23
-3x = 0 + -23

Combine like terms: 0 + -23 = -23
-3x = -23

Divide each side by '-3'.
x = 7.666666667

Simplifying
x = 7.666666667
Solution
x = {1, 7.666666667}

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