(5x-3)(5x-3)-11(4x+1)=1

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Solution for (5x-3)(5x-3)-11(4x+1)=1 equation: 


Simplifying
(5x + -3)(5x + -3) + -11(4x + 1) = 1

Reorder the terms:
(-3 + 5x)(5x + -3) + -11(4x + 1) = 1

Reorder the terms:
(-3 + 5x)(-3 + 5x) + -11(4x + 1) = 1

Multiply (-3 + 5x) * (-3 + 5x)
(-3(-3 + 5x) + 5x * (-3 + 5x)) + -11(4x + 1) = 1
((-3 * -3 + 5x * -3) + 5x * (-3 + 5x)) + -11(4x + 1) = 1
((9 + -15x) + 5x * (-3 + 5x)) + -11(4x + 1) = 1
(9 + -15x + (-3 * 5x + 5x * 5x)) + -11(4x + 1) = 1
(9 + -15x + (-15x + 25x2)) + -11(4x + 1) = 1

Combine like terms: -15x + -15x = -30x
(9 + -30x + 25x2) + -11(4x + 1) = 1

Reorder the terms:
9 + -30x + 25x2 + -11(1 + 4x) = 1
9 + -30x + 25x2 + (1 * -11 + 4x * -11) = 1
9 + -30x + 25x2 + (-11 + -44x) = 1

Reorder the terms:
9 + -11 + -30x + -44x + 25x2 = 1

Combine like terms: 9 + -11 = -2
-2 + -30x + -44x + 25x2 = 1

Combine like terms: -30x + -44x = -74x
-2 + -74x + 25x2 = 1

Solving
-2 + -74x + 25x2 = 1

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + -74x + 25x2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + -74x + 25x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + -74x + 25x2 = 0

Factor a trinomial.
(-1 + -25x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -25x)' equal to zero and attempt to solve:

Simplifying
-1 + -25x = 0

Solving
-1 + -25x = 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 + -25x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -25x = 0 + 1
-25x = 0 + 1

Combine like terms: 0 + 1 = 1
-25x = 1

Divide each side by '-25'.
x = -0.04

Simplifying
x = -0.04

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.04, 3}

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