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

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


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

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

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

Multiply (-4 + 7X) * (5 + 4X)
2(-4(5 + 4X) + 7X * (5 + 4X)) = 0
2((5 * -4 + 4X * -4) + 7X * (5 + 4X)) = 0
2((-20 + -16X) + 7X * (5 + 4X)) = 0
2(-20 + -16X + (5 * 7X + 4X * 7X)) = 0
2(-20 + -16X + (35X + 28X2)) = 0

Combine like terms: -16X + 35X = 19X
2(-20 + 19X + 28X2) = 0
(-20 * 2 + 19X * 2 + 28X2 * 2) = 0
(-40 + 38X + 56X2) = 0

Solving
-40 + 38X + 56X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 19X + 28X2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -4X)' equal to zero and attempt to solve:

Simplifying
-5 + -4X = 0

Solving
-5 + -4X = 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 + -4X = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4X = 0 + 5
-4X = 0 + 5

Combine like terms: 0 + 5 = 5
-4X = 5

Divide each side by '-4'.
X = -1.25

Simplifying
X = -1.25

Subproblem 2
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
Solution
X = {-1.25, 0.5714285714}

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