2(5x-9)=3(bx-6)+4x

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Solution for 2(5x-9)=3(bx-6)+4x equation: 


Simplifying
2(5x + -9) = 3(bx + -6) + 4x

Reorder the terms:
2(-9 + 5x) = 3(bx + -6) + 4x
(-9 * 2 + 5x * 2) = 3(bx + -6) + 4x
(-18 + 10x) = 3(bx + -6) + 4x

Reorder the terms:
-18 + 10x = 3(-6 + bx) + 4x
-18 + 10x = (-6 * 3 + bx * 3) + 4x
-18 + 10x = (-18 + 3bx) + 4x

Add '18' to each side of the equation.
-18 + 18 + 10x = -18 + 3bx + 18 + 4x

Combine like terms: -18 + 18 = 0
0 + 10x = -18 + 3bx + 18 + 4x
10x = -18 + 3bx + 18 + 4x

Reorder the terms:
10x = -18 + 18 + 3bx + 4x

Combine like terms: -18 + 18 = 0
10x = 0 + 3bx + 4x
10x = 3bx + 4x

Solving
10x = 3bx + 4x

Solving for variable 'x'.

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

Add '-3bx' to each side of the equation.
-3bx + 10x = 3bx + -3bx + 4x

Combine like terms: 3bx + -3bx = 0
-3bx + 10x = 0 + 4x
-3bx + 10x = 4x

Add '-4x' to each side of the equation.
-3bx + 10x + -4x = 4x + -4x

Combine like terms: 10x + -4x = 6x
-3bx + 6x = 4x + -4x

Combine like terms: 4x + -4x = 0
-3bx + 6x = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1b + 2) = 0

Ignore the factor 3.

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 '(-1b + 2)' equal to zero and attempt to solve:

Simplifying
-1b + 2 = 0

Reorder the terms:
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Add 'b' to each side of the equation.
-1b + b = -2 + b

Combine like terms: -1b + b = 0
0 = -2 + b

Simplifying
0 = -2 + b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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