(2x-3)(5y+7)=2(5x-6)(y+1)

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Solution for (2x-3)(5y+7)=2(5x-6)(y+1) equation:


Simplifying
(2x + -3)(5y + 7) = 2(5x + -6)(y + 1)

Reorder the terms:
(-3 + 2x)(5y + 7) = 2(5x + -6)(y + 1)

Reorder the terms:
(-3 + 2x)(7 + 5y) = 2(5x + -6)(y + 1)

Multiply (-3 + 2x) * (7 + 5y)
(-3(7 + 5y) + 2x * (7 + 5y)) = 2(5x + -6)(y + 1)
((7 * -3 + 5y * -3) + 2x * (7 + 5y)) = 2(5x + -6)(y + 1)
((-21 + -15y) + 2x * (7 + 5y)) = 2(5x + -6)(y + 1)
(-21 + -15y + (7 * 2x + 5y * 2x)) = 2(5x + -6)(y + 1)
(-21 + -15y + (14x + 10xy)) = 2(5x + -6)(y + 1)

Reorder the terms:
(-21 + 14x + 10xy + -15y) = 2(5x + -6)(y + 1)
(-21 + 14x + 10xy + -15y) = 2(5x + -6)(y + 1)

Reorder the terms:
-21 + 14x + 10xy + -15y = 2(-6 + 5x)(y + 1)

Reorder the terms:
-21 + 14x + 10xy + -15y = 2(-6 + 5x)(1 + y)

Multiply (-6 + 5x) * (1 + y)
-21 + 14x + 10xy + -15y = 2(-6(1 + y) + 5x * (1 + y))
-21 + 14x + 10xy + -15y = 2((1 * -6 + y * -6) + 5x * (1 + y))
-21 + 14x + 10xy + -15y = 2((-6 + -6y) + 5x * (1 + y))
-21 + 14x + 10xy + -15y = 2(-6 + -6y + (1 * 5x + y * 5x))
-21 + 14x + 10xy + -15y = 2(-6 + -6y + (5x + 5xy))

Reorder the terms:
-21 + 14x + 10xy + -15y = 2(-6 + 5x + 5xy + -6y)
-21 + 14x + 10xy + -15y = 2(-6 + 5x + 5xy + -6y)
-21 + 14x + 10xy + -15y = (-6 * 2 + 5x * 2 + 5xy * 2 + -6y * 2)
-21 + 14x + 10xy + -15y = (-12 + 10x + 10xy + -12y)

Add '-10xy' to each side of the equation.
-21 + 14x + 10xy + -10xy + -15y = -12 + 10x + 10xy + -10xy + -12y

Combine like terms: 10xy + -10xy = 0
-21 + 14x + 0 + -15y = -12 + 10x + 10xy + -10xy + -12y
-21 + 14x + -15y = -12 + 10x + 10xy + -10xy + -12y

Combine like terms: 10xy + -10xy = 0
-21 + 14x + -15y = -12 + 10x + 0 + -12y
-21 + 14x + -15y = -12 + 10x + -12y

Solving
-21 + 14x + -15y = -12 + 10x + -12y

Solving for variable 'x'.

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

Add '-10x' to each side of the equation.
-21 + 14x + -10x + -15y = -12 + 10x + -10x + -12y

Combine like terms: 14x + -10x = 4x
-21 + 4x + -15y = -12 + 10x + -10x + -12y

Combine like terms: 10x + -10x = 0
-21 + 4x + -15y = -12 + 0 + -12y
-21 + 4x + -15y = -12 + -12y

Add '21' to each side of the equation.
-21 + 4x + 21 + -15y = -12 + 21 + -12y

Reorder the terms:
-21 + 21 + 4x + -15y = -12 + 21 + -12y

Combine like terms: -21 + 21 = 0
0 + 4x + -15y = -12 + 21 + -12y
4x + -15y = -12 + 21 + -12y

Combine like terms: -12 + 21 = 9
4x + -15y = 9 + -12y

Add '15y' to each side of the equation.
4x + -15y + 15y = 9 + -12y + 15y

Combine like terms: -15y + 15y = 0
4x + 0 = 9 + -12y + 15y
4x = 9 + -12y + 15y

Combine like terms: -12y + 15y = 3y
4x = 9 + 3y

Divide each side by '4'.
x = 2.25 + 0.75y

Simplifying
x = 2.25 + 0.75y

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