4x(3x+6)=5x(x+2)

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Solution for 4x(3x+6)=5x(x+2) equation: 


Simplifying
4x(3x + 6) = 5x(x + 2)

Reorder the terms:
4x(6 + 3x) = 5x(x + 2)
(6 * 4x + 3x * 4x) = 5x(x + 2)
(24x + 12x2) = 5x(x + 2)

Reorder the terms:
24x + 12x2 = 5x(2 + x)
24x + 12x2 = (2 * 5x + x * 5x)
24x + 12x2 = (10x + 5x2)

Solving
24x + 12x2 = 10x + 5x2

Solving for variable 'x'.

Reorder the terms:
24x + -10x + 12x2 + -5x2 = 10x + 5x2 + -10x + -5x2

Combine like terms: 24x + -10x = 14x
14x + 12x2 + -5x2 = 10x + 5x2 + -10x + -5x2

Combine like terms: 12x2 + -5x2 = 7x2
14x + 7x2 = 10x + 5x2 + -10x + -5x2

Reorder the terms:
14x + 7x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
14x + 7x2 = 0 + 5x2 + -5x2
14x + 7x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
14x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(2 + x) = 0

Ignore the factor 7.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, -2}

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