2x^2-9x+4=(2x-1)(2x-1)

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Solution for 2x^2-9x+4=(2x-1)(2x-1) equation: 


Simplifying
2x2 + -9x + 4 = (2x + -1)(2x + -1)

Reorder the terms:
4 + -9x + 2x2 = (2x + -1)(2x + -1)

Reorder the terms:
4 + -9x + 2x2 = (-1 + 2x)(2x + -1)

Reorder the terms:
4 + -9x + 2x2 = (-1 + 2x)(-1 + 2x)

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

Combine like terms: -2x + -2x = -4x
4 + -9x + 2x2 = (1 + -4x + 4x2)

Solving
4 + -9x + 2x2 = 1 + -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
4 + -1 + -9x + 4x + 2x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2

Combine like terms: 4 + -1 = 3
3 + -9x + 4x + 2x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2

Combine like terms: -9x + 4x = -5x
3 + -5x + 2x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
3 + -5x + -2x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2

Reorder the terms:
3 + -5x + -2x2 = 1 + -1 + -4x + 4x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
3 + -5x + -2x2 = 0 + -4x + 4x + 4x2 + -4x2
3 + -5x + -2x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
3 + -5x + -2x2 = 0 + 4x2 + -4x2
3 + -5x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -5x + -2x2 = 0

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


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {0.5, -3}

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