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

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


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

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

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

Multiply (-5 + 3x) * (7 + 6x)
(-5(7 + 6x) + 3x * (7 + 6x)) = 0
((7 * -5 + 6x * -5) + 3x * (7 + 6x)) = 0
((-35 + -30x) + 3x * (7 + 6x)) = 0
(-35 + -30x + (7 * 3x + 6x * 3x)) = 0
(-35 + -30x + (21x + 18x2)) = 0

Combine like terms: -30x + 21x = -9x
(-35 + -9x + 18x2) = 0

Solving
-35 + -9x + 18x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-7 + -6x)' equal to zero and attempt to solve: Simplifying -7 + -6x = 0 Solving -7 + -6x = 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 + -6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x = 0 + 7 -6x = 0 + 7 Combine like terms: 0 + 7 = 7 -6x = 7 Divide each side by '-6'. x = -1.166666667 Simplifying x = -1.166666667

Subproblem 2

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-1.166666667, 1.666666667}

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