(2x+3)(x-4)=(x-6)(2x-3)

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


Simplifying
(2x + 3)(x + -4) = (x + -6)(2x + -3)

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

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

Multiply (3 + 2x) * (-4 + x)
(3(-4 + x) + 2x * (-4 + x)) = (x + -6)(2x + -3)
((-4 * 3 + x * 3) + 2x * (-4 + x)) = (x + -6)(2x + -3)
((-12 + 3x) + 2x * (-4 + x)) = (x + -6)(2x + -3)
(-12 + 3x + (-4 * 2x + x * 2x)) = (x + -6)(2x + -3)
(-12 + 3x + (-8x + 2x2)) = (x + -6)(2x + -3)

Combine like terms: 3x + -8x = -5x
(-12 + -5x + 2x2) = (x + -6)(2x + -3)

Reorder the terms:
-12 + -5x + 2x2 = (-6 + x)(2x + -3)

Reorder the terms:
-12 + -5x + 2x2 = (-6 + x)(-3 + 2x)

Multiply (-6 + x) * (-3 + 2x)
-12 + -5x + 2x2 = (-6(-3 + 2x) + x(-3 + 2x))
-12 + -5x + 2x2 = ((-3 * -6 + 2x * -6) + x(-3 + 2x))
-12 + -5x + 2x2 = ((18 + -12x) + x(-3 + 2x))
-12 + -5x + 2x2 = (18 + -12x + (-3 * x + 2x * x))
-12 + -5x + 2x2 = (18 + -12x + (-3x + 2x2))

Combine like terms: -12x + -3x = -15x
-12 + -5x + 2x2 = (18 + -15x + 2x2)

Add '-2x2' to each side of the equation.
-12 + -5x + 2x2 + -2x2 = 18 + -15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -5x + 0 = 18 + -15x + 2x2 + -2x2
-12 + -5x = 18 + -15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -5x = 18 + -15x + 0
-12 + -5x = 18 + -15x

Solving
-12 + -5x = 18 + -15x

Solving for variable 'x'.

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

Add '15x' to each side of the equation.
-12 + -5x + 15x = 18 + -15x + 15x

Combine like terms: -5x + 15x = 10x
-12 + 10x = 18 + -15x + 15x

Combine like terms: -15x + 15x = 0
-12 + 10x = 18 + 0
-12 + 10x = 18

Add '12' to each side of the equation.
-12 + 12 + 10x = 18 + 12

Combine like terms: -12 + 12 = 0
0 + 10x = 18 + 12
10x = 18 + 12

Combine like terms: 18 + 12 = 30
10x = 30

Divide each side by '10'.
x = 3

Simplifying
x = 3

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