2x(3x-7)+3x(x-1)=4x(2x-3)

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Solution for 2x(3x-7)+3x(x-1)=4x(2x-3) equation: 


Simplifying
2x(3x + -7) + 3x(x + -1) = 4x(2x + -3)

Reorder the terms:
2x(-7 + 3x) + 3x(x + -1) = 4x(2x + -3)
(-7 * 2x + 3x * 2x) + 3x(x + -1) = 4x(2x + -3)
(-14x + 6x2) + 3x(x + -1) = 4x(2x + -3)

Reorder the terms:
-14x + 6x2 + 3x(-1 + x) = 4x(2x + -3)
-14x + 6x2 + (-1 * 3x + x * 3x) = 4x(2x + -3)
-14x + 6x2 + (-3x + 3x2) = 4x(2x + -3)

Reorder the terms:
-14x + -3x + 6x2 + 3x2 = 4x(2x + -3)

Combine like terms: -14x + -3x = -17x
-17x + 6x2 + 3x2 = 4x(2x + -3)

Combine like terms: 6x2 + 3x2 = 9x2
-17x + 9x2 = 4x(2x + -3)

Reorder the terms:
-17x + 9x2 = 4x(-3 + 2x)
-17x + 9x2 = (-3 * 4x + 2x * 4x)
-17x + 9x2 = (-12x + 8x2)

Solving
-17x + 9x2 = -12x + 8x2

Solving for variable 'x'.

Reorder the terms:
-17x + 12x + 9x2 + -8x2 = -12x + 8x2 + 12x + -8x2

Combine like terms: -17x + 12x = -5x
-5x + 9x2 + -8x2 = -12x + 8x2 + 12x + -8x2

Combine like terms: 9x2 + -8x2 = 1x2
-5x + 1x2 = -12x + 8x2 + 12x + -8x2

Reorder the terms:
-5x + 1x2 = -12x + 12x + 8x2 + -8x2

Combine like terms: -12x + 12x = 0
-5x + 1x2 = 0 + 8x2 + -8x2
-5x + 1x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-5x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, 5}

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