2x(3x-1)+7=7(2-3x)

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Solution for 2x(3x-1)+7=7(2-3x) equation: 


Simplifying
2x(3x + -1) + 7 = 7(2 + -3x)

Reorder the terms:
2x(-1 + 3x) + 7 = 7(2 + -3x)
(-1 * 2x + 3x * 2x) + 7 = 7(2 + -3x)
(-2x + 6x2) + 7 = 7(2 + -3x)

Reorder the terms:
7 + -2x + 6x2 = 7(2 + -3x)
7 + -2x + 6x2 = (2 * 7 + -3x * 7)
7 + -2x + 6x2 = (14 + -21x)

Solving
7 + -2x + 6x2 = 14 + -21x

Solving for variable 'x'.

Reorder the terms:
7 + -14 + -2x + 21x + 6x2 = 14 + -21x + -14 + 21x

Combine like terms: 7 + -14 = -7
-7 + -2x + 21x + 6x2 = 14 + -21x + -14 + 21x

Combine like terms: -2x + 21x = 19x
-7 + 19x + 6x2 = 14 + -21x + -14 + 21x

Reorder the terms:
-7 + 19x + 6x2 = 14 + -14 + -21x + 21x

Combine like terms: 14 + -14 = 0
-7 + 19x + 6x2 = 0 + -21x + 21x
-7 + 19x + 6x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
-7 + 19x + 6x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-3.5, 0.3333333333}

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