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

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


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

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

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

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

Combine like terms: 28x + -1x = 27x
(-7 + 27x + 4x2) = 0

Solving
-7 + 27x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 0.25}

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