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

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


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

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

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

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

Combine like terms: -16x + 35x = 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((-5 + -4x)(4 + -7x)) = 0

Ignore the factor 5.

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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