(2x-3)(3x+1)=(3x-4)(2x-2)

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Solution for (2x-3)(3x+1)=(3x-4)(2x-2) equation:


Simplifying
(2x + -3)(3x + 1) = (3x + -4)(2x + -2)

Reorder the terms:
(-3 + 2x)(3x + 1) = (3x + -4)(2x + -2)

Reorder the terms:
(-3 + 2x)(1 + 3x) = (3x + -4)(2x + -2)

Multiply (-3 + 2x) * (1 + 3x)
(-3(1 + 3x) + 2x * (1 + 3x)) = (3x + -4)(2x + -2)
((1 * -3 + 3x * -3) + 2x * (1 + 3x)) = (3x + -4)(2x + -2)
((-3 + -9x) + 2x * (1 + 3x)) = (3x + -4)(2x + -2)
(-3 + -9x + (1 * 2x + 3x * 2x)) = (3x + -4)(2x + -2)
(-3 + -9x + (2x + 6x2)) = (3x + -4)(2x + -2)

Combine like terms: -9x + 2x = -7x
(-3 + -7x + 6x2) = (3x + -4)(2x + -2)

Reorder the terms:
-3 + -7x + 6x2 = (-4 + 3x)(2x + -2)

Reorder the terms:
-3 + -7x + 6x2 = (-4 + 3x)(-2 + 2x)

Multiply (-4 + 3x) * (-2 + 2x)
-3 + -7x + 6x2 = (-4(-2 + 2x) + 3x * (-2 + 2x))
-3 + -7x + 6x2 = ((-2 * -4 + 2x * -4) + 3x * (-2 + 2x))
-3 + -7x + 6x2 = ((8 + -8x) + 3x * (-2 + 2x))
-3 + -7x + 6x2 = (8 + -8x + (-2 * 3x + 2x * 3x))
-3 + -7x + 6x2 = (8 + -8x + (-6x + 6x2))

Combine like terms: -8x + -6x = -14x
-3 + -7x + 6x2 = (8 + -14x + 6x2)

Add '-6x2' to each side of the equation.
-3 + -7x + 6x2 + -6x2 = 8 + -14x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-3 + -7x + 0 = 8 + -14x + 6x2 + -6x2
-3 + -7x = 8 + -14x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-3 + -7x = 8 + -14x + 0
-3 + -7x = 8 + -14x

Solving
-3 + -7x = 8 + -14x

Solving for variable 'x'.

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

Add '14x' to each side of the equation.
-3 + -7x + 14x = 8 + -14x + 14x

Combine like terms: -7x + 14x = 7x
-3 + 7x = 8 + -14x + 14x

Combine like terms: -14x + 14x = 0
-3 + 7x = 8 + 0
-3 + 7x = 8

Add '3' to each side of the equation.
-3 + 3 + 7x = 8 + 3

Combine like terms: -3 + 3 = 0
0 + 7x = 8 + 3
7x = 8 + 3

Combine like terms: 8 + 3 = 11
7x = 11

Divide each side by '7'.
x = 1.571428571

Simplifying
x = 1.571428571

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