6(5x-3)(5x+7)=0

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Solution for 6(5x-3)(5x+7)=0 equation: 


Simplifying
6(5x + -3)(5x + 7) = 0

Reorder the terms:
6(-3 + 5x)(5x + 7) = 0

Reorder the terms:
6(-3 + 5x)(7 + 5x) = 0

Multiply (-3 + 5x) * (7 + 5x)
6(-3(7 + 5x) + 5x * (7 + 5x)) = 0
6((7 * -3 + 5x * -3) + 5x * (7 + 5x)) = 0
6((-21 + -15x) + 5x * (7 + 5x)) = 0
6(-21 + -15x + (7 * 5x + 5x * 5x)) = 0
6(-21 + -15x + (35x + 25x2)) = 0

Combine like terms: -15x + 35x = 20x
6(-21 + 20x + 25x2) = 0
(-21 * 6 + 20x * 6 + 25x2 * 6) = 0
(-126 + 120x + 150x2) = 0

Solving
-126 + 120x + 150x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 20x + 25x2) = 0

Factor a trinomial.
6((-7 + -5x)(3 + -5x)) = 0

Ignore the factor 6.

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 '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-1.4, 0.6}

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