4(3x-5)(6x+7)=0

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Solution for 4(3x-5)(6x+7)=0 equation: 


Simplifying
4(3x + -5)(6x + 7) = 0

Reorder the terms:
4(-5 + 3x)(6x + 7) = 0

Reorder the terms:
4(-5 + 3x)(7 + 6x) = 0

Multiply (-5 + 3x) * (7 + 6x)
4(-5(7 + 6x) + 3x * (7 + 6x)) = 0
4((7 * -5 + 6x * -5) + 3x * (7 + 6x)) = 0
4((-35 + -30x) + 3x * (7 + 6x)) = 0
4(-35 + -30x + (7 * 3x + 6x * 3x)) = 0
4(-35 + -30x + (21x + 18x2)) = 0

Combine like terms: -30x + 21x = -9x
4(-35 + -9x + 18x2) = 0
(-35 * 4 + -9x * 4 + 18x2 * 4) = 0
(-140 + -36x + 72x2) = 0

Solving
-140 + -36x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + -9x + 18x2) = 0

Factor a trinomial.
4((-7 + -6x)(5 + -3x)) = 0

Ignore the factor 4.

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 '(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
Solution
x = {-1.166666667, 1.666666667}

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