(3-2x)(3+2x)+10x=1-x^2

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Solution for (3-2x)(3+2x)+10x=1-x^2 equation: 


Simplifying
(3 + -2x)(3 + 2x) + 10x = 1 + -1x2

Multiply (3 + -2x) * (3 + 2x)
(3(3 + 2x) + -2x * (3 + 2x)) + 10x = 1 + -1x2
((3 * 3 + 2x * 3) + -2x * (3 + 2x)) + 10x = 1 + -1x2
((9 + 6x) + -2x * (3 + 2x)) + 10x = 1 + -1x2
(9 + 6x + (3 * -2x + 2x * -2x)) + 10x = 1 + -1x2
(9 + 6x + (-6x + -4x2)) + 10x = 1 + -1x2

Combine like terms: 6x + -6x = 0
(9 + 0 + -4x2) + 10x = 1 + -1x2
(9 + -4x2) + 10x = 1 + -1x2

Reorder the terms:
9 + 10x + -4x2 = 1 + -1x2

Solving
9 + 10x + -4x2 = 1 + -1x2

Solving for variable 'x'.

Reorder the terms:
9 + -1 + 10x + -4x2 + x2 = 1 + -1x2 + -1 + x2

Combine like terms: 9 + -1 = 8
8 + 10x + -4x2 + x2 = 1 + -1x2 + -1 + x2

Combine like terms: -4x2 + x2 = -3x2
8 + 10x + -3x2 = 1 + -1x2 + -1 + x2

Reorder the terms:
8 + 10x + -3x2 = 1 + -1 + -1x2 + x2

Combine like terms: 1 + -1 = 0
8 + 10x + -3x2 = 0 + -1x2 + x2
8 + 10x + -3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
8 + 10x + -3x2 = 0

Factor a trinomial.
(4 + -1x)(2 + 3x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {4, -0.6666666667}

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