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

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


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

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

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

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

Multiply (-7 + 6x) * (5 + 3x)
x(-7(5 + 3x) + 6x * (5 + 3x)) = 0
x((5 * -7 + 3x * -7) + 6x * (5 + 3x)) = 0
x((-35 + -21x) + 6x * (5 + 3x)) = 0
x(-35 + -21x + (5 * 6x + 3x * 6x)) = 0
x(-35 + -21x + (30x + 18x2)) = 0

Combine like terms: -21x + 30x = 9x
x(-35 + 9x + 18x2) = 0
(-35 * x + 9x * x + 18x2 * x) = 0
(-35x + 9x2 + 18x3) = 0

Solving
-35x + 9x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + 9x + 18x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

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

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

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 3
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 = {0, -1.666666667, 1.166666667}

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