(3x+7)(5x+6)=0

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


Simplifying
(3x + 7)(5x + 6) = 0

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

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

Multiply (7 + 3x) * (6 + 5x)
(7(6 + 5x) + 3x * (6 + 5x)) = 0
((6 * 7 + 5x * 7) + 3x * (6 + 5x)) = 0
((42 + 35x) + 3x * (6 + 5x)) = 0
(42 + 35x + (6 * 3x + 5x * 3x)) = 0
(42 + 35x + (18x + 15x2)) = 0

Combine like terms: 35x + 18x = 53x
(42 + 53x + 15x2) = 0

Solving
42 + 53x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 3x)(6 + 5x) = 0

Subproblem 1

Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333

Subproblem 2

Set the factor '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Divide each side by '5'. x = -1.2 Simplifying x = -1.2

Solution

x = {-2.333333333, -1.2}

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