(7x-4)(7x-4)=49

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Solution for (7x-4)(7x-4)=49 equation: 


Simplifying
(7x + -4)(7x + -4) = 49

Reorder the terms:
(-4 + 7x)(7x + -4) = 49

Reorder the terms:
(-4 + 7x)(-4 + 7x) = 49

Multiply (-4 + 7x) * (-4 + 7x)
(-4(-4 + 7x) + 7x * (-4 + 7x)) = 49
((-4 * -4 + 7x * -4) + 7x * (-4 + 7x)) = 49
((16 + -28x) + 7x * (-4 + 7x)) = 49
(16 + -28x + (-4 * 7x + 7x * 7x)) = 49
(16 + -28x + (-28x + 49x2)) = 49

Combine like terms: -28x + -28x = -56x
(16 + -56x + 49x2) = 49

Solving
16 + -56x + 49x2 = 49

Solving for variable 'x'.

Reorder the terms:
16 + -49 + -56x + 49x2 = 49 + -49

Combine like terms: 16 + -49 = -33
-33 + -56x + 49x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-33 + -56x + 49x2 = 0

Factor a trinomial.
(-3 + -7x)(11 + -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 '(11 + -7x)' equal to zero and attempt to solve:

Simplifying
11 + -7x = 0

Solving
11 + -7x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -7x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7x = 0 + -11
-7x = 0 + -11

Combine like terms: 0 + -11 = -11
-7x = -11

Divide each side by '-7'.
x = 1.571428571

Simplifying
x = 1.571428571
Solution
x = {-0.4285714286, 1.571428571}

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