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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.25, 7}

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