(4x^2-3x)(6x+5)=0

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Solution for (4x^2-3x)(6x+5)=0 equation:


Simplifying
(4x2 + -3x)(6x + 5) = 0

Reorder the terms:
(-3x + 4x2)(6x + 5) = 0

Reorder the terms:
(-3x + 4x2)(5 + 6x) = 0

Multiply (-3x + 4x2) * (5 + 6x)
(-3x * (5 + 6x) + 4x2 * (5 + 6x)) = 0
((5 * -3x + 6x * -3x) + 4x2 * (5 + 6x)) = 0
((-15x + -18x2) + 4x2 * (5 + 6x)) = 0
(-15x + -18x2 + (5 * 4x2 + 6x * 4x2)) = 0
(-15x + -18x2 + (20x2 + 24x3)) = 0

Combine like terms: -18x2 + 20x2 = 2x2
(-15x + 2x2 + 24x3) = 0

Solving
-15x + 2x2 + 24x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((-5 + -6x)(3 + -4x)) = 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 + -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 3
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, -0.8333333333, 0.75}

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