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

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


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

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

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

Multiply (-2 + 7x) * (5 + 4x)
4(-2(5 + 4x) + 7x * (5 + 4x)) = 0
4((5 * -2 + 4x * -2) + 7x * (5 + 4x)) = 0
4((-10 + -8x) + 7x * (5 + 4x)) = 0
4(-10 + -8x + (5 * 7x + 4x * 7x)) = 0
4(-10 + -8x + (35x + 28x2)) = 0

Combine like terms: -8x + 35x = 27x
4(-10 + 27x + 28x2) = 0
(-10 * 4 + 27x * 4 + 28x2 * 4) = 0
(-40 + 108x + 112x2) = 0

Solving
-40 + 108x + 112x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 27x + 28x2) = 0

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

Ignore the factor 4.

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 '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-1.25, 0.2857142857}

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