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

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


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

Reorder the terms:
4(-1 + 7x) + (7x + -1)(7x + -1) = 0
(-1 * 4 + 7x * 4) + (7x + -1)(7x + -1) = 0
(-4 + 28x) + (7x + -1)(7x + -1) = 0

Reorder the terms:
-4 + 28x + (-1 + 7x)(7x + -1) = 0

Reorder the terms:
-4 + 28x + (-1 + 7x)(-1 + 7x) = 0

Multiply (-1 + 7x) * (-1 + 7x)
-4 + 28x + (-1(-1 + 7x) + 7x * (-1 + 7x)) = 0
-4 + 28x + ((-1 * -1 + 7x * -1) + 7x * (-1 + 7x)) = 0
-4 + 28x + ((1 + -7x) + 7x * (-1 + 7x)) = 0
-4 + 28x + (1 + -7x + (-1 * 7x + 7x * 7x)) = 0
-4 + 28x + (1 + -7x + (-7x + 49x2)) = 0

Combine like terms: -7x + -7x = -14x
-4 + 28x + (1 + -14x + 49x2) = 0

Reorder the terms:
-4 + 1 + 28x + -14x + 49x2 = 0

Combine like terms: -4 + 1 = -3
-3 + 28x + -14x + 49x2 = 0

Combine like terms: 28x + -14x = 14x
-3 + 14x + 49x2 = 0

Solving
-3 + 14x + 49x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -7x)(1 + -7x) = 0


Subproblem 1
Set the factor '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

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

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

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-0.4285714286, 0.1428571429}

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