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

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


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

Reorder the terms:
6x(-7 + 3x) = 7(7 + -3x)
(-7 * 6x + 3x * 6x) = 7(7 + -3x)
(-42x + 18x2) = 7(7 + -3x)
-42x + 18x2 = (7 * 7 + -3x * 7)
-42x + 18x2 = (49 + -21x)

Solving
-42x + 18x2 = 49 + -21x

Solving for variable 'x'.

Reorder the terms:
-49 + -42x + 21x + 18x2 = 49 + -21x + -49 + 21x

Combine like terms: -42x + 21x = -21x
-49 + -21x + 18x2 = 49 + -21x + -49 + 21x

Reorder the terms:
-49 + -21x + 18x2 = 49 + -49 + -21x + 21x

Combine like terms: 49 + -49 = 0
-49 + -21x + 18x2 = 0 + -21x + 21x
-49 + -21x + 18x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
-49 + -21x + 18x2 = 0

Factor a trinomial.
(-7 + -6x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 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 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.166666667, 2.333333333}

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