12x(x-3)+1=6(x+1)-5

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Solution for 12x(x-3)+1=6(x+1)-5 equation: 


Simplifying
12x(x + -3) + 1 = 6(x + 1) + -5

Reorder the terms:
12x(-3 + x) + 1 = 6(x + 1) + -5
(-3 * 12x + x * 12x) + 1 = 6(x + 1) + -5
(-36x + 12x2) + 1 = 6(x + 1) + -5

Reorder the terms:
1 + -36x + 12x2 = 6(x + 1) + -5

Reorder the terms:
1 + -36x + 12x2 = 6(1 + x) + -5
1 + -36x + 12x2 = (1 * 6 + x * 6) + -5
1 + -36x + 12x2 = (6 + 6x) + -5

Reorder the terms:
1 + -36x + 12x2 = 6 + -5 + 6x

Combine like terms: 6 + -5 = 1
1 + -36x + 12x2 = 1 + 6x

Add '-1' to each side of the equation.
1 + -36x + -1 + 12x2 = 1 + -1 + 6x

Reorder the terms:
1 + -1 + -36x + 12x2 = 1 + -1 + 6x

Combine like terms: 1 + -1 = 0
0 + -36x + 12x2 = 1 + -1 + 6x
-36x + 12x2 = 1 + -1 + 6x

Combine like terms: 1 + -1 = 0
-36x + 12x2 = 0 + 6x
-36x + 12x2 = 6x

Solving
-36x + 12x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-36x + -6x + 12x2 = 6x + -6x

Combine like terms: -36x + -6x = -42x
-42x + 12x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-42x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-7 + 2x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 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 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 3.5}

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