3x(4x+2)=2x(5x+7)

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Solution for 3x(4x+2)=2x(5x+7) equation: 


Simplifying
3x(4x + 2) = 2x(5x + 7)

Reorder the terms:
3x(2 + 4x) = 2x(5x + 7)
(2 * 3x + 4x * 3x) = 2x(5x + 7)
(6x + 12x2) = 2x(5x + 7)

Reorder the terms:
6x + 12x2 = 2x(7 + 5x)
6x + 12x2 = (7 * 2x + 5x * 2x)
6x + 12x2 = (14x + 10x2)

Solving
6x + 12x2 = 14x + 10x2

Solving for variable 'x'.

Reorder the terms:
6x + -14x + 12x2 + -10x2 = 14x + 10x2 + -14x + -10x2

Combine like terms: 6x + -14x = -8x
-8x + 12x2 + -10x2 = 14x + 10x2 + -14x + -10x2

Combine like terms: 12x2 + -10x2 = 2x2
-8x + 2x2 = 14x + 10x2 + -14x + -10x2

Reorder the terms:
-8x + 2x2 = 14x + -14x + 10x2 + -10x2

Combine like terms: 14x + -14x = 0
-8x + 2x2 = 0 + 10x2 + -10x2
-8x + 2x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + x) = 0

Ignore the factor 2.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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