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

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


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

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

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

Multiply (-5 + 4x) * (4 + 7x)
5(-5(4 + 7x) + 4x * (4 + 7x)) = 0
5((4 * -5 + 7x * -5) + 4x * (4 + 7x)) = 0
5((-20 + -35x) + 4x * (4 + 7x)) = 0
5(-20 + -35x + (4 * 4x + 7x * 4x)) = 0
5(-20 + -35x + (16x + 28x2)) = 0

Combine like terms: -35x + 16x = -19x
5(-20 + -19x + 28x2) = 0
(-20 * 5 + -19x * 5 + 28x2 * 5) = 0
(-100 + -95x + 140x2) = 0

Solving
-100 + -95x + 140x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -19x + 28x2) = 0

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

Ignore the factor 5.

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 + -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
Solution
x = {-0.5714285714, 1.25}

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