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

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


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

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

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

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

Combine like terms: -35x + 42x = 7x
5(-49 + 7x + 30x2) = 0
(-49 * 5 + 7x * 5 + 30x2 * 5) = 0
(-245 + 35x + 150x2) = 0

Solving
-245 + 35x + 150x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-49 + 7x + 30x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.4, 1.166666667}

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