(4x-1)(6x+7)=0

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Solution for (4x-1)(6x+7)=0 equation:


Simplifying
(4x + -1)(6x + 7) = 0

Reorder the terms:
(-1 + 4x)(6x + 7) = 0

Reorder the terms:
(-1 + 4x)(7 + 6x) = 0

Multiply (-1 + 4x) * (7 + 6x)
(-1(7 + 6x) + 4x * (7 + 6x)) = 0
((7 * -1 + 6x * -1) + 4x * (7 + 6x)) = 0
((-7 + -6x) + 4x * (7 + 6x)) = 0
(-7 + -6x + (7 * 4x + 6x * 4x)) = 0
(-7 + -6x + (28x + 24x2)) = 0

Combine like terms: -6x + 28x = 22x
(-7 + 22x + 24x2) = 0

Solving
-7 + 22x + 24x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(1 + -4x) = 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 '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Solution

x = {-1.166666667, 0.25}

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