6(2x-5)(7x+4)=0

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Solution for 6(2x-5)(7x+4)=0 equation: 


Simplifying
6(2x + -5)(7x + 4) = 0

Reorder the terms:
6(-5 + 2x)(7x + 4) = 0

Reorder the terms:
6(-5 + 2x)(4 + 7x) = 0

Multiply (-5 + 2x) * (4 + 7x)
6(-5(4 + 7x) + 2x * (4 + 7x)) = 0
6((4 * -5 + 7x * -5) + 2x * (4 + 7x)) = 0
6((-20 + -35x) + 2x * (4 + 7x)) = 0
6(-20 + -35x + (4 * 2x + 7x * 2x)) = 0
6(-20 + -35x + (8x + 14x2)) = 0

Combine like terms: -35x + 8x = -27x
6(-20 + -27x + 14x2) = 0
(-20 * 6 + -27x * 6 + 14x2 * 6) = 0
(-120 + -162x + 84x2) = 0

Solving
-120 + -162x + 84x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + -27x + 14x2) = 0

Factor a trinomial.
6((-4 + -7x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

Solving
-4 + -7x = 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 + -7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7x = 0 + 4
-7x = 0 + 4

Combine like terms: 0 + 4 = 4
-7x = 4

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.5714285714, 2.5}

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