(5x-1)(6x+8)=0

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Solution for (5x-1)(6x+8)=0 equation: 


Simplifying
(5x + -1)(6x + 8) = 0

Reorder the terms:
(-1 + 5x)(6x + 8) = 0

Reorder the terms:
(-1 + 5x)(8 + 6x) = 0

Multiply (-1 + 5x) * (8 + 6x)
(-1(8 + 6x) + 5x * (8 + 6x)) = 0
((8 * -1 + 6x * -1) + 5x * (8 + 6x)) = 0
((-8 + -6x) + 5x * (8 + 6x)) = 0
(-8 + -6x + (8 * 5x + 6x * 5x)) = 0
(-8 + -6x + (40x + 30x2)) = 0

Combine like terms: -6x + 40x = 34x
(-8 + 34x + 30x2) = 0

Solving
-8 + 34x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 17x + 15x2) = 0

Factor a trinomial.
2((-4 + -3x)(1 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

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

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

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-1.333333333, 0.2}

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