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

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


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

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

Reorder the terms:
14x + 7x2 = 3x(1 + x)
14x + 7x2 = (1 * 3x + x * 3x)
14x + 7x2 = (3x + 3x2)

Solving
14x + 7x2 = 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
14x + -3x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 14x + -3x = 11x
11x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 7x2 + -3x2 = 4x2
11x + 4x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
11x + 4x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
11x + 4x2 = 0 + 3x2 + -3x2
11x + 4x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
11x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + 4x) = 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 '(11 + 4x)' equal to zero and attempt to solve:

Simplifying
11 + 4x = 0

Solving
11 + 4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 4x = 0 + -11
4x = 0 + -11

Combine like terms: 0 + -11 = -11
4x = -11

Divide each side by '4'.
x = -2.75

Simplifying
x = -2.75
Solution
x = {0, -2.75}

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