4(5-6x)(8x+9)=0

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Solution for 4(5-6x)(8x+9)=0 equation: 


Simplifying
4(5 + -6x)(8x + 9) = 0

Reorder the terms:
4(5 + -6x)(9 + 8x) = 0

Multiply (5 + -6x) * (9 + 8x)
4(5(9 + 8x) + -6x * (9 + 8x)) = 0
4((9 * 5 + 8x * 5) + -6x * (9 + 8x)) = 0
4((45 + 40x) + -6x * (9 + 8x)) = 0
4(45 + 40x + (9 * -6x + 8x * -6x)) = 0
4(45 + 40x + (-54x + -48x2)) = 0

Combine like terms: 40x + -54x = -14x
4(45 + -14x + -48x2) = 0
(45 * 4 + -14x * 4 + -48x2 * 4) = 0
(180 + -56x + -192x2) = 0

Solving
180 + -56x + -192x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -14x + -48x2) = 0

Factor a trinomial.
4((5 + -6x)(9 + 8x)) = 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 '(9 + 8x)' equal to zero and attempt to solve:

Simplifying
9 + 8x = 0

Solving
9 + 8x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 8x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8x = 0 + -9
8x = 0 + -9

Combine like terms: 0 + -9 = -9
8x = -9

Divide each side by '8'.
x = -1.125

Simplifying
x = -1.125
Solution
x = {0.8333333333, -1.125}

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