6(3x-5)+3(4x-5)=15(ax-b)

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Solution for 6(3x-5)+3(4x-5)=15(ax-b) equation:


Simplifying
6(3x + -5) + 3(4x + -5) = 15(ax + -1b)

Reorder the terms:
6(-5 + 3x) + 3(4x + -5) = 15(ax + -1b)
(-5 * 6 + 3x * 6) + 3(4x + -5) = 15(ax + -1b)
(-30 + 18x) + 3(4x + -5) = 15(ax + -1b)

Reorder the terms:
-30 + 18x + 3(-5 + 4x) = 15(ax + -1b)
-30 + 18x + (-5 * 3 + 4x * 3) = 15(ax + -1b)
-30 + 18x + (-15 + 12x) = 15(ax + -1b)

Reorder the terms:
-30 + -15 + 18x + 12x = 15(ax + -1b)

Combine like terms: -30 + -15 = -45
-45 + 18x + 12x = 15(ax + -1b)

Combine like terms: 18x + 12x = 30x
-45 + 30x = 15(ax + -1b)
-45 + 30x = (ax * 15 + -1b * 15)
-45 + 30x = (15ax + -15b)

Solving
-45 + 30x = 15ax + -15b

Solving for variable 'x'.

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

Add '-15ax' to each side of the equation.
-45 + -15ax + 30x = 15ax + -15ax + -15b

Combine like terms: 15ax + -15ax = 0
-45 + -15ax + 30x = 0 + -15b
-45 + -15ax + 30x = -15b

Add '45' to each side of the equation.
-45 + -15ax + 45 + 30x = 45 + -15b

Reorder the terms:
-45 + 45 + -15ax + 30x = 45 + -15b

Combine like terms: -45 + 45 = 0
0 + -15ax + 30x = 45 + -15b
-15ax + 30x = 45 + -15b

Reorder the terms:
-45 + -15ax + 15b + 30x = 45 + -15b + -45 + 15b

Reorder the terms:
-45 + -15ax + 15b + 30x = 45 + -45 + -15b + 15b

Combine like terms: 45 + -45 = 0
-45 + -15ax + 15b + 30x = 0 + -15b + 15b
-45 + -15ax + 15b + 30x = -15b + 15b

Combine like terms: -15b + 15b = 0
-45 + -15ax + 15b + 30x = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-3 + -1ax + b + 2x) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(-3 + -1ax + b + 2x)' equal to zero and attempt to solve: Simplifying -3 + -1ax + b + 2x = 0 Solving -3 + -1ax + b + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1ax + b + 3 + 2x = 0 + 3 Reorder the terms: -3 + 3 + -1ax + b + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1ax + b + 2x = 0 + 3 -1ax + b + 2x = 0 + 3 Combine like terms: 0 + 3 = 3 -1ax + b + 2x = 3 Add '-1b' to each side of the equation. -1ax + b + -1b + 2x = 3 + -1b Combine like terms: b + -1b = 0 -1ax + 0 + 2x = 3 + -1b -1ax + 2x = 3 + -1b The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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