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

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


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

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

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

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

Combine like terms: -35x + 8x = -27x
2(-14 + -27x + 20x2) = 0
(-14 * 2 + -27x * 2 + 20x2 * 2) = 0
(-28 + -54x + 40x2) = 0

Solving
-28 + -54x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -27x + 20x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

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

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

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-0.4, 1.75}

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