6x(x-3)=x+7

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Solution for 6x(x-3)=x+7 equation: 


Simplifying
6x(x + -3) = x + 7

Reorder the terms:
6x(-3 + x) = x + 7
(-3 * 6x + x * 6x) = x + 7
(-18x + 6x2) = x + 7

Reorder the terms:
-18x + 6x2 = 7 + x

Solving
-18x + 6x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -18x + -1x + 6x2 = 7 + x + -7 + -1x

Combine like terms: -18x + -1x = -19x
-7 + -19x + 6x2 = 7 + x + -7 + -1x

Reorder the terms:
-7 + -19x + 6x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-7 + -19x + 6x2 = 0 + x + -1x
-7 + -19x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-7 + -19x + 6x2 = 0

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


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 + -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 = {-0.3333333333, 3.5}

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