(3x-2)(3x+2)=3x(x-1)+5

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Solution for (3x-2)(3x+2)=3x(x-1)+5 equation:


Simplifying
(3x + -2)(3x + 2) = 3x(x + -1) + 5

Reorder the terms:
(-2 + 3x)(3x + 2) = 3x(x + -1) + 5

Reorder the terms:
(-2 + 3x)(2 + 3x) = 3x(x + -1) + 5

Multiply (-2 + 3x) * (2 + 3x)
(-2(2 + 3x) + 3x * (2 + 3x)) = 3x(x + -1) + 5
((2 * -2 + 3x * -2) + 3x * (2 + 3x)) = 3x(x + -1) + 5
((-4 + -6x) + 3x * (2 + 3x)) = 3x(x + -1) + 5
(-4 + -6x + (2 * 3x + 3x * 3x)) = 3x(x + -1) + 5
(-4 + -6x + (6x + 9x2)) = 3x(x + -1) + 5

Combine like terms: -6x + 6x = 0
(-4 + 0 + 9x2) = 3x(x + -1) + 5
(-4 + 9x2) = 3x(x + -1) + 5

Reorder the terms:
-4 + 9x2 = 3x(-1 + x) + 5
-4 + 9x2 = (-1 * 3x + x * 3x) + 5
-4 + 9x2 = (-3x + 3x2) + 5

Reorder the terms:
-4 + 9x2 = 5 + -3x + 3x2

Solving
-4 + 9x2 = 5 + -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4 + -5 + 3x + 9x2 + -3x2 = 5 + -3x + 3x2 + -5 + 3x + -3x2

Combine like terms: -4 + -5 = -9
-9 + 3x + 9x2 + -3x2 = 5 + -3x + 3x2 + -5 + 3x + -3x2

Combine like terms: 9x2 + -3x2 = 6x2
-9 + 3x + 6x2 = 5 + -3x + 3x2 + -5 + 3x + -3x2

Reorder the terms:
-9 + 3x + 6x2 = 5 + -5 + -3x + 3x + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-9 + 3x + 6x2 = 0 + -3x + 3x + 3x2 + -3x2
-9 + 3x + 6x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
-9 + 3x + 6x2 = 0 + 3x2 + -3x2
-9 + 3x + 6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9 + 3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

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

Solution

x = {-1.5, 1}

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