4(4x^2-20x+25)-(9x^2+6x+1)=0

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Solution for 4(4x^2-20x+25)-(9x^2+6x+1)=0 equation:


Simplifying
4(4x2 + -20x + 25) + -1(9x2 + 6x + 1) = 0

Reorder the terms:
4(25 + -20x + 4x2) + -1(9x2 + 6x + 1) = 0
(25 * 4 + -20x * 4 + 4x2 * 4) + -1(9x2 + 6x + 1) = 0
(100 + -80x + 16x2) + -1(9x2 + 6x + 1) = 0

Reorder the terms:
100 + -80x + 16x2 + -1(1 + 6x + 9x2) = 0
100 + -80x + 16x2 + (1 * -1 + 6x * -1 + 9x2 * -1) = 0
100 + -80x + 16x2 + (-1 + -6x + -9x2) = 0

Reorder the terms:
100 + -1 + -80x + -6x + 16x2 + -9x2 = 0

Combine like terms: 100 + -1 = 99
99 + -80x + -6x + 16x2 + -9x2 = 0

Combine like terms: -80x + -6x = -86x
99 + -86x + 16x2 + -9x2 = 0

Combine like terms: 16x2 + -9x2 = 7x2
99 + -86x + 7x2 = 0

Solving
99 + -86x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -7x)(11 + -1x) = 0

Subproblem 1

Set the factor '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 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 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {1.285714286, 11}

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