12x(5x+2)-15y(5x+2)=21(5x+2)

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Solution for 12x(5x+2)-15y(5x+2)=21(5x+2) equation: 


Simplifying
12x(5x + 2) + -15y(5x + 2) = 21(5x + 2)

Reorder the terms:
12x(2 + 5x) + -15y(5x + 2) = 21(5x + 2)
(2 * 12x + 5x * 12x) + -15y(5x + 2) = 21(5x + 2)
(24x + 60x2) + -15y(5x + 2) = 21(5x + 2)

Reorder the terms:
24x + 60x2 + -15y(2 + 5x) = 21(5x + 2)
24x + 60x2 + (2 * -15y + 5x * -15y) = 21(5x + 2)

Reorder the terms:
24x + 60x2 + (-75xy + -30y) = 21(5x + 2)
24x + 60x2 + (-75xy + -30y) = 21(5x + 2)

Reorder the terms:
24x + -75xy + 60x2 + -30y = 21(5x + 2)

Reorder the terms:
24x + -75xy + 60x2 + -30y = 21(2 + 5x)
24x + -75xy + 60x2 + -30y = (2 * 21 + 5x * 21)
24x + -75xy + 60x2 + -30y = (42 + 105x)

Solving
24x + -75xy + 60x2 + -30y = 42 + 105x

Solving for variable 'x'.

Reorder the terms:
-42 + 24x + -105x + -75xy + 60x2 + -30y = 42 + 105x + -42 + -105x

Combine like terms: 24x + -105x = -81x
-42 + -81x + -75xy + 60x2 + -30y = 42 + 105x + -42 + -105x

Reorder the terms:
-42 + -81x + -75xy + 60x2 + -30y = 42 + -42 + 105x + -105x

Combine like terms: 42 + -42 = 0
-42 + -81x + -75xy + 60x2 + -30y = 0 + 105x + -105x
-42 + -81x + -75xy + 60x2 + -30y = 105x + -105x

Combine like terms: 105x + -105x = 0
-42 + -81x + -75xy + 60x2 + -30y = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -27x + -25xy + 20x2 + -10y) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-14 + -27x + -25xy + 20x2 + -10y)' equal to zero and attempt to solve:

Simplifying
-14 + -27x + -25xy + 20x2 + -10y = 0

Solving
-14 + -27x + -25xy + 20x2 + -10y = 0

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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