(2x+1)(x-4)=x^2-4x-6

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Solution for (2x+1)(x-4)=x^2-4x-6 equation:


Simplifying
(2x + 1)(x + -4) = x2 + -4x + -6

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

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

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = x2 + -4x + -6
((-4 * 1 + x * 1) + 2x * (-4 + x)) = x2 + -4x + -6
((-4 + 1x) + 2x * (-4 + x)) = x2 + -4x + -6
(-4 + 1x + (-4 * 2x + x * 2x)) = x2 + -4x + -6
(-4 + 1x + (-8x + 2x2)) = x2 + -4x + -6

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) = x2 + -4x + -6

Reorder the terms:
-4 + -7x + 2x2 = -6 + -4x + x2

Solving
-4 + -7x + 2x2 = -6 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + -7x + 4x + 2x2 + -1x2 = -6 + -4x + x2 + 6 + 4x + -1x2

Combine like terms: -4 + 6 = 2
2 + -7x + 4x + 2x2 + -1x2 = -6 + -4x + x2 + 6 + 4x + -1x2

Combine like terms: -7x + 4x = -3x
2 + -3x + 2x2 + -1x2 = -6 + -4x + x2 + 6 + 4x + -1x2

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

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

Combine like terms: -6 + 6 = 0
2 + -3x + 1x2 = 0 + -4x + 4x + x2 + -1x2
2 + -3x + 1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
2 + -3x + 1x2 = 0 + x2 + -1x2
2 + -3x + 1x2 = x2 + -1x2

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

Factor a trinomial.
(1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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