6x(2x-1)=9x+2(2-x)

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Solution for 6x(2x-1)=9x+2(2-x) equation: 


Simplifying
6x(2x + -1) = 9x + 2(2 + -1x)

Reorder the terms:
6x(-1 + 2x) = 9x + 2(2 + -1x)
(-1 * 6x + 2x * 6x) = 9x + 2(2 + -1x)
(-6x + 12x2) = 9x + 2(2 + -1x)
-6x + 12x2 = 9x + (2 * 2 + -1x * 2)
-6x + 12x2 = 9x + (4 + -2x)

Reorder the terms:
-6x + 12x2 = 4 + 9x + -2x

Combine like terms: 9x + -2x = 7x
-6x + 12x2 = 4 + 7x

Solving
-6x + 12x2 = 4 + 7x

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + -7x + 12x2 = 4 + 7x + -4 + -7x

Combine like terms: -6x + -7x = -13x
-4 + -13x + 12x2 = 4 + 7x + -4 + -7x

Reorder the terms:
-4 + -13x + 12x2 = 4 + -4 + 7x + -7x

Combine like terms: 4 + -4 = 0
-4 + -13x + 12x2 = 0 + 7x + -7x
-4 + -13x + 12x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-4 + -13x + 12x2 = 0

Factor a trinomial.
(-1 + -4x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-0.25, 1.333333333}

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