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

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


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

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

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

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

Combine like terms: -15x + 24x = 9x
4(-18 + 9x + 20x2) = 0
(-18 * 4 + 9x * 4 + 20x2 * 4) = 0
(-72 + 36x + 80x2) = 0

Solving
-72 + 36x + 80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 9x + 20x2) = 0

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

Ignore the factor 4.

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

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

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

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

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

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 = {-1.2, 0.75}

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