(7x-6)(-7x-5)+14x-12=0

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Solution for (7x-6)(-7x-5)+14x-12=0 equation:


Simplifying
(7x + -6)(-7x + -5) + 14x + -12 = 0

Reorder the terms:
(-6 + 7x)(-7x + -5) + 14x + -12 = 0

Reorder the terms:
(-6 + 7x)(-5 + -7x) + 14x + -12 = 0

Multiply (-6 + 7x) * (-5 + -7x)
(-6(-5 + -7x) + 7x * (-5 + -7x)) + 14x + -12 = 0
((-5 * -6 + -7x * -6) + 7x * (-5 + -7x)) + 14x + -12 = 0
((30 + 42x) + 7x * (-5 + -7x)) + 14x + -12 = 0
(30 + 42x + (-5 * 7x + -7x * 7x)) + 14x + -12 = 0
(30 + 42x + (-35x + -49x2)) + 14x + -12 = 0

Combine like terms: 42x + -35x = 7x
(30 + 7x + -49x2) + 14x + -12 = 0

Reorder the terms:
30 + -12 + 7x + 14x + -49x2 = 0

Combine like terms: 30 + -12 = 18
18 + 7x + 14x + -49x2 = 0

Combine like terms: 7x + 14x = 21x
18 + 21x + -49x2 = 0

Solving
18 + 21x + -49x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(3 + 7x)' equal to zero and attempt to solve: Simplifying 3 + 7x = 0 Solving 3 + 7x = 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 + 7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x = 0 + -3 7x = 0 + -3 Combine like terms: 0 + -3 = -3 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286

Solution

x = {0.8571428571, -0.4285714286}

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