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

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


Simplifying
-1(2x + 3)(7x + 6) = 0

Reorder the terms:
-1(3 + 2x)(7x + 6) = 0

Reorder the terms:
-1(3 + 2x)(6 + 7x) = 0

Multiply (3 + 2x) * (6 + 7x)
-1(3(6 + 7x) + 2x * (6 + 7x)) = 0
-1((6 * 3 + 7x * 3) + 2x * (6 + 7x)) = 0
-1((18 + 21x) + 2x * (6 + 7x)) = 0
-1(18 + 21x + (6 * 2x + 7x * 2x)) = 0
-1(18 + 21x + (12x + 14x2)) = 0

Combine like terms: 21x + 12x = 33x
-1(18 + 33x + 14x2) = 0
(18 * -1 + 33x * -1 + 14x2 * -1) = 0
(-18 + -33x + -14x2) = 0

Solving
-18 + -33x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 33x + 14x2) = 0

Factor a trinomial.
-1((3 + 2x)(6 + 7x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 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 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Divide each side by '7'. x = -0.8571428571 Simplifying x = -0.8571428571

Solution

x = {-1.5, -0.8571428571}

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