7x(x+2)+6=3x(x+1)

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Solution for 7x(x+2)+6=3x(x+1) equation: 


Simplifying
7x(x + 2) + 6 = 3x(x + 1)

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

Reorder the terms:
6 + 14x + 7x2 = 3x(x + 1)

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

Solving
6 + 14x + 7x2 = 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
6 + 14x + -3x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 14x + -3x = 11x
6 + 11x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 7x2 + -3x2 = 4x2
6 + 11x + 4x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
6 + 11x + 4x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
6 + 11x + 4x2 = 0 + 3x2 + -3x2
6 + 11x + 4x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + 11x + 4x2 = 0

Factor a trinomial.
(2 + x)(3 + 4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-2, -0.75}

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