What is the answer to (x-1)|x^2-4x+3|+2x^2+3x-5=0 ?

The answer to (x-1)|x^2-4x+3|+2x^2+3x-5=0 is x=1

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(x-1)|x^2-4x+3|+2x^2+3x-5=0

(x - 1) x^{2} - 4 x + 3 + 2 x^{2} + 3 x - 5 = 0

x = 1

Solution steps

(x - 1) x^{2} - 4 x + 3 + 2 x^{2} + 3 x - 5 = 0

Find positive and negative intervals

x \leq 1, 1 < x < 3, x \geq 3

Solve the inequality for each interval

x = 1 or No Solution

x = 1

∣ 2 x - 1 ∣ = ∣ x + 3 ∣

- 2 x^{2} - 8 x = 10

∣ x - 3 ∣ = ∣ 2 x - 1 ∣

∣ 2 x - 3 ∣ + ∣ 2 x + 1 ∣ + ∣ 2 x + 5 ∣ = 12

5 ∣ x + 3 ∣ - 1 = 6

What is the answer to (x-1)|x^2-4x+3|+2x^2+3x-5=0 ?
The answer to (x-1)|x^2-4x+3|+2x^2+3x-5=0 is x=1
Solve for x: (x-1)|x^2-4x+3|+2x^2+3x-5=0
The solution is x=1