(4x-1)(7x+8)=0

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Solution for (4x-1)(7x+8)=0 equation: 


Simplifying
(4x + -1)(7x + 8) = 0

Reorder the terms:
(-1 + 4x)(7x + 8) = 0

Reorder the terms:
(-1 + 4x)(8 + 7x) = 0

Multiply (-1 + 4x) * (8 + 7x)
(-1(8 + 7x) + 4x * (8 + 7x)) = 0
((8 * -1 + 7x * -1) + 4x * (8 + 7x)) = 0
((-8 + -7x) + 4x * (8 + 7x)) = 0
(-8 + -7x + (8 * 4x + 7x * 4x)) = 0
(-8 + -7x + (32x + 28x2)) = 0

Combine like terms: -7x + 32x = 25x
(-8 + 25x + 28x2) = 0

Solving
-8 + 25x + 28x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(1 + -4x) = 0


Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

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 = {-1.142857143, 0.25}

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