4x(x+1)=3x(x+2)-1

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Solution for 4x(x+1)=3x(x+2)-1 equation:


Simplifying
4x(x + 1) = 3x(x + 2) + -1

Reorder the terms:
4x(1 + x) = 3x(x + 2) + -1
(1 * 4x + x * 4x) = 3x(x + 2) + -1
(4x + 4x2) = 3x(x + 2) + -1

Reorder the terms:
4x + 4x2 = 3x(2 + x) + -1
4x + 4x2 = (2 * 3x + x * 3x) + -1
4x + 4x2 = (6x + 3x2) + -1

Reorder the terms:
4x + 4x2 = -1 + 6x + 3x2

Solving
4x + 4x2 = -1 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
1 + 4x + -6x + 4x2 + -3x2 = -1 + 6x + 3x2 + 1 + -6x + -3x2

Combine like terms: 4x + -6x = -2x
1 + -2x + 4x2 + -3x2 = -1 + 6x + 3x2 + 1 + -6x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
1 + -2x + 1x2 = -1 + 6x + 3x2 + 1 + -6x + -3x2

Reorder the terms:
1 + -2x + 1x2 = -1 + 1 + 6x + -6x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
1 + -2x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2
1 + -2x + 1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
1 + -2x + 1x2 = 0 + 3x2 + -3x2
1 + -2x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
1 + -2x + 1x2 = 0

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


Subproblem 1
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

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, 1}

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