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

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


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

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

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

Multiply (-3 + 4x) * (5 + 6x)
4(-3(5 + 6x) + 4x * (5 + 6x)) = 0
4((5 * -3 + 6x * -3) + 4x * (5 + 6x)) = 0
4((-15 + -18x) + 4x * (5 + 6x)) = 0
4(-15 + -18x + (5 * 4x + 6x * 4x)) = 0
4(-15 + -18x + (20x + 24x2)) = 0

Combine like terms: -18x + 20x = 2x
4(-15 + 2x + 24x2) = 0
(-15 * 4 + 2x * 4 + 24x2 * 4) = 0
(-60 + 8x + 96x2) = 0

Solving
-60 + 8x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 2x + 24x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.8333333333, 0.75}

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