(2x-9)²=(2x-3)(2x+3) equation

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(2*x - 9)  = (2*x - 3)*(2*x + 3)

$$\left(2 x - 9\right)^{2} = \left(2 x - 3\right) \left(2 x + 3\right)$$

Simplify

Detail solution

Given the equation:

(2*x-9)^2 = (2*x-3)*(2*x+3)

Expand expressions:

81 - 36*x + 4*x^2 = (2*x-3)*(2*x+3)

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

Reducing, you get:

90 - 36*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 36 x = -90$$
Divide both parts of the equation by -36

x = -90 / (-36)

We get the answer: x = 5/2

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

x1 = 5/2

$$x_{1} = \frac{5}{2}$$

x1 = 5/2

Sum and product of roots [src]

sum

5/2

$$\frac{5}{2}$$

5/2

$$\frac{5}{2}$$

product

5/2

$$\frac{5}{2}$$

5/2

$$\frac{5}{2}$$

5/2

Numerical answer [src]

x1 = 2.5

x1 = 2.5