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

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


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

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

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

Multiply (7 + 6x) * (-7 + 5x)
(7(-7 + 5x) + 6x * (-7 + 5x)) = 0
((-7 * 7 + 5x * 7) + 6x * (-7 + 5x)) = 0
((-49 + 35x) + 6x * (-7 + 5x)) = 0
(-49 + 35x + (-7 * 6x + 5x * 6x)) = 0
(-49 + 35x + (-42x + 30x2)) = 0

Combine like terms: 35x + -42x = -7x
(-49 + -7x + 30x2) = 0

Solving
-49 + -7x + 30x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(7 + -5x) = 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 '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4

Solution

x = {-1.166666667, 1.4}

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