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

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


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

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

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

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

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

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

Solving
-11x + -4x2 = 6

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11x + 4x2) = 0

Factor a trinomial.
-1((2 + x)(3 + 4x)) = 0

Ignore the factor -1.

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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