(3x+2)(5x+7)-6x-4=0

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Solution for (3x+2)(5x+7)-6x-4=0 equation: 


Simplifying
(3x + 2)(5x + 7) + -6x + -4 = 0

Reorder the terms:
(2 + 3x)(5x + 7) + -6x + -4 = 0

Reorder the terms:
(2 + 3x)(7 + 5x) + -6x + -4 = 0

Multiply (2 + 3x) * (7 + 5x)
(2(7 + 5x) + 3x * (7 + 5x)) + -6x + -4 = 0
((7 * 2 + 5x * 2) + 3x * (7 + 5x)) + -6x + -4 = 0
((14 + 10x) + 3x * (7 + 5x)) + -6x + -4 = 0
(14 + 10x + (7 * 3x + 5x * 3x)) + -6x + -4 = 0
(14 + 10x + (21x + 15x2)) + -6x + -4 = 0

Combine like terms: 10x + 21x = 31x
(14 + 31x + 15x2) + -6x + -4 = 0

Reorder the terms:
14 + -4 + 31x + -6x + 15x2 = 0

Combine like terms: 14 + -4 = 10
10 + 31x + -6x + 15x2 = 0

Combine like terms: 31x + -6x = 25x
10 + 25x + 15x2 = 0

Solving
10 + 25x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 5x + 3x2) = 0

Factor a trinomial.
5((1 + x)(2 + 3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-1, -0.6666666667}

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