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

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


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

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

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

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

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

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

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

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

Multiply (-6 + 4x) * (-6 + x)
-6x + 4x2 = (-6(-6 + x) + 4x * (-6 + x))
-6x + 4x2 = ((-6 * -6 + x * -6) + 4x * (-6 + x))
-6x + 4x2 = ((36 + -6x) + 4x * (-6 + x))
-6x + 4x2 = (36 + -6x + (-6 * 4x + x * 4x))
-6x + 4x2 = (36 + -6x + (-24x + 4x2))

Combine like terms: -6x + -24x = -30x
-6x + 4x2 = (36 + -30x + 4x2)

Add '-4x2' to each side of the equation.
-6x + 4x2 + -4x2 = 36 + -30x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x + 0 = 36 + -30x + 4x2 + -4x2
-6x = 36 + -30x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x = 36 + -30x + 0
-6x = 36 + -30x

Solving
-6x = 36 + -30x

Solving for variable 'x'.

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

Add '30x' to each side of the equation.
-6x + 30x = 36 + -30x + 30x

Combine like terms: -6x + 30x = 24x
24x = 36 + -30x + 30x

Combine like terms: -30x + 30x = 0
24x = 36 + 0
24x = 36

Divide each side by '24'.
x = 1.5

Simplifying
x = 1.5

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