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

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


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

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

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

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

Combine like terms: -30x + 35x = 5x
(-35 + 5x + 30x2) = 0

Solving
-35 + 5x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + x + 6x2) = 0

Factor a trinomial.
5((-7 + -6x)(1 + -1x)) = 0

Ignore the factor 5.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.166666667, 1}

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