2(3x-5)(7x+4)=0

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Solution for 2(3x-5)(7x+4)=0 equation: 


Simplifying
2(3x + -5)(7x + 4) = 0

Reorder the terms:
2(-5 + 3x)(7x + 4) = 0

Reorder the terms:
2(-5 + 3x)(4 + 7x) = 0

Multiply (-5 + 3x) * (4 + 7x)
2(-5(4 + 7x) + 3x * (4 + 7x)) = 0
2((4 * -5 + 7x * -5) + 3x * (4 + 7x)) = 0
2((-20 + -35x) + 3x * (4 + 7x)) = 0
2(-20 + -35x + (4 * 3x + 7x * 3x)) = 0
2(-20 + -35x + (12x + 21x2)) = 0

Combine like terms: -35x + 12x = -23x
2(-20 + -23x + 21x2) = 0
(-20 * 2 + -23x * 2 + 21x2 * 2) = 0
(-40 + -46x + 42x2) = 0

Solving
-40 + -46x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -23x + 21x2) = 0

Factor a trinomial.
2((-4 + -7x)(5 + -3x)) = 0

Ignore the factor 2.

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 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.5714285714, 1.666666667}

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