7(4x-1)(2x+5)=0

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Solution for 7(4x-1)(2x+5)=0 equation: 


Simplifying
7(4x + -1)(2x + 5) = 0

Reorder the terms:
7(-1 + 4x)(2x + 5) = 0

Reorder the terms:
7(-1 + 4x)(5 + 2x) = 0

Multiply (-1 + 4x) * (5 + 2x)
7(-1(5 + 2x) + 4x * (5 + 2x)) = 0
7((5 * -1 + 2x * -1) + 4x * (5 + 2x)) = 0
7((-5 + -2x) + 4x * (5 + 2x)) = 0
7(-5 + -2x + (5 * 4x + 2x * 4x)) = 0
7(-5 + -2x + (20x + 8x2)) = 0

Combine like terms: -2x + 20x = 18x
7(-5 + 18x + 8x2) = 0
(-5 * 7 + 18x * 7 + 8x2 * 7) = 0
(-35 + 126x + 56x2) = 0

Solving
-35 + 126x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + 18x + 8x2) = 0

Factor a trinomial.
7((-5 + -2x)(1 + -4x)) = 0

Ignore the factor 7.

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-2.5, 0.25}

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